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The International 

Bureau of 
Weights and 
Measures 

1875-1975 



""EAU of 



U.S. DEPARTMENT OF COMMERCE 
National Bureau of Standards 

NBS SPECIAL PUBLICATION 420 



Aerial view of the Pavilion de Breteuil and the immediate environs. To the east, the Seine and 
the Pont de Sevres; to the northwest, the Pare de Saint-Cloud: between the Pavilion de 
Breteuil (circled) and the bridge: the Manufacture Nationale de Porcelaine de Sevres. The 
new laboratories (1964) are situated north of the circle and are scarcely visible; they were 
built in a way to preserve the countryside. (Document Institute (leographique National, 
Paris). 




Medal commeiiKiraUn-i the centennial (if the Convention cif tlie Metre and the International 
Bureau of Weights and Measures. (Desifined by R. Corbin. Monnaie de Paris) 



The International Bureau 

of Weights and Measures 1875-1975 



Edited by 
Chester H. Page 

National Bureau of Standards, U.S.A. 
and 

Pan I Vigoiireiix 

National Physieal Laboratory, U.K. 

Translation of tlie 

BIPM Centennial Volume 



Piibli>lieH on the ocrasioii <>( the 
lOOth Aniiiver^ai y ol tlie 
Treaty of tlie Metre 
May 20, 1975 




U.S. DEPARTMENT OF COMMERCE 

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Direcior 
Issued May 1 975 



National Bureau of Standards Special Publication 420 

Nat. Bur. Stand. (U.S.), Spec. Publ. 420. 256 pages (May 1975) 
CODEN: XNBSAV 



U.S. GOVERNMENT PRINTING OFFICE 
WASHINGTON: 1975 



For sale by the Superintendent of Documents 
U.S. Government Printing Office, Washington, D.C. 20402 
Paper cover Price $3.00 
Stock Number 003-003-01408 
Catalog Number C13.10:420 



FOREWORD 



The metric system was made legal by Congress in 1866, the United 
States of America signed the Treaty of the Metre in 1875, and we have been 
active in international coordination of measurements since that time. In 
science, in pharmacology, and increasingly in industry, the United States 
is making ever greater use of the International System of Units (SI). 

In view of this ongoing conversion to the metric system, the celebra- 
tion of both the Centennial of the Treaty and the first century of metrology 
at the International Bureau of Weights and Measures (BIPM) holds con- 
siderable interest for the American public. It therefore gives me great plea- 
sure to make available this translation of the BIPM's official centennial 
volume. 




Richard W. Roberts 

Director, National Bureau of Standards 



III 



THE INTERNATIONAL BUREAU OF WEIGHTS AND 
MEASURES AT THE TIME OF ITS CENTENNIAL 



We have all heard of the International Bureau of Weights and Mea- 
sures; it is even one of the memories which have been part of us since our 
school days. And it is still more true in countries other than France, without 
doubt because there is added to the prestige of the "Standard Metre" and 
the "Standard Kilogram," that of the metric system conceived by the Paris 
Academy of Sciences under the French Revolution. 

The International Bureau of Weights and Measures is situated on 
French ground, but it is independent of France: decisions concerning it 
rest with a Conference which assembles the delegates of 43 countries, 
furthermore, the 18 members of the Committee elected by the Conference, 
who constitute, with the Director of the Bureau, its operations directorate, 
must be scientific persons of entirely different nationalities. These 43 
countries contribute, each its share, to the operating expenses of the 
BIPM, which was therefore since the beginning, and still is, truly interna- 
tional. 

That which characterizes the BIPM now, at the time of its centennial, 
is the blending of permanence, which comes from its mission, and of rapid 
renovation, as in the techniques used to accomplish this mission. Its per- 
manent mission is to achieve uniformity of physical measurements 
throughout the world, at the highest level of precision; this uniformity, 
recognized as necessary as early as 1875, has become even more so since 
the advent of the rapid scientific and industrial progress which dominates 
our civilization. As for the level of precision, it raises itself today, by virtue 
of the discoveries in atomic physics, to a degree which would have been in- 
conceivable 10 or 20 years earlier; the former standards of a mechanical 
nature tend to be replaced by standards of an atomic nature controlled by 

rigorous universal quantum laws. This is why the BIPM needs a staff of an 
ever higher scientific level: additionally, its technical equipment must be 
regularly updated. Thus, in the fields where it specializes narrowly, the 
BIPM keeps itself at the level of the best metrological laboratories in the 
world. 

The BIPM furnishes standards to countries needing them, compares 
the standards of countries which are sufficiently advanced to establish 
their own standards, and contributes to research looking forward to the still 
higher precision of the future; it serves as a neutral and impartial scientific 
arbiter when national sensitivities impede an international agreement. It is 



v 



also a center for discussion, for coordination, and for preparation of inter- 
national decisions, whenever these decisions concern standards, for exam- 
ple, those of length and time (change of the definition of the metre in 1960 
and of the second in 1967), or the International System of Units, developed 
from the Metric System. The importance of the mission of the BIPM is well 
illustrated by the progressive adoption, in all countries, of the International 
System of Units; despite the force of habit which retards change, this 
system is spreading inevitably on its own merits, and is supplanting the 
multiplicity of disparate units which we have too long endured. 

In the present volume, the chapter on the measurement units of the 
International System of Units is due to Professor Jan de Boer (University of 
Amsterdam), Secretary of the International Committee on Weights and 
Measures. The history is by H. Moreau, metrological editor of the BIPM. 
The following chapters discuss the principal laboratory activities of the 
BIPM; they have been composed by its scientific staff. An editing commit- 
tee, consisting of J. Bonhoure, P. Carre, G. Leclerc, A. Rytz. and P. 
Giacomo, deputy director, has seen to making them homogeneous in 
presentation and so easily readable that a large number of readers can ab- 
sorb the most important aspects of the basic metrology, often ignored, 
sometimes even by scientists. 



J. Terrien 
Director, BIPM 



VI 



CONTENTS 



Page 



Foreword HI 

The International Bureau of Weights and Measures 

at the time of its centennial, by J. Terrien V 

From the earlier systems of measures to the 

International System of Units, by J, de Boer 1 

I. HISTORICAL INTRODUCTION 21 

The Metre Convention and its organs 21 

A century of metrology 29 

II. MASS 43 

The Prototype Kilograms and periodic verifications 43 

Determination of the mass of Kilograms outside the periodic verifications 48 

Balances and methods used for the comparison of Kilograms, auxiliary 

measurements 50 

Recent balances and current studies 54 

III. LENGTH 65 

Measurements of length based on the International Metre 66 

Toward the change of the definition of the metre 72 

Putting the 1 960 definition of the metre into practice 77 

Complementary studies of the standard radiation 88 

Lasers 92 

IV. GRAVIMETRY 103 

Metrological importance of the i<nowledge of the acceleration of gravity 1 03 

Reversible pendulums 103 

Free fall of a graduated scale 104 

Method of two stations 106 

V. MANOBAROMETRY 117 

VI. THERMOMETRY 125 

The gas thermometer and the mercury thermometer 125 

The International Practical Temperature Scale 1 26 

Pyrometric study of the freezing-point temperature of gold 131 

VII. ELECTRICITY 135 

Electric units 1 36 

Standards 137 

Installations of the BIPM 140 

Periodic international comparisons 1 45 

Maintenance of the ohm and the volt by the BIPM 151 

Progress of metrology in the field of electricity 1 54 

VIII. PHOTOMETRY 163 

Apparatus and measurement methods at the BIPM 164 

International comparisons of intensity and of luminous flux 170 

Maintenance of the units and stability of the standard lamps 173 

Spectrophotometric measurements 173 

International comparison of distribution temperature scales 1 75 

Prospects offered by radiometry 1 75 



VII 



IX MEASUREMENT OF RADIOACTIVITY 179 

Generalities on the methods of measurement 1 79 

The method of counting by 4 tt/? (PC)- 7 coincidences 180 

The BIPM laboratory for radionuclide measurements 181 

Radioactivity standards 183 

International comparisons of radionuclides 1 84 

Statistics of counting 185 

Energy measurement: alpha-particle spectrometry 190 

X. X AND GAMMA RAYS 197 

Generalities 1 97 

Measurement of X Radiation 200 

Measurement of Gamma Radiation 203 

XL NEUTRON MEASUREMENTS 213 

Generalities 213 

Measurement of the emission rate of a neutron source 

by the manganous sulfate bath method 215 

Comparative measurements of neutron sources 218 

Measurement of the flux density of a source of fast monoenergetic neutrons 221 

Appendixes 

1 . Convention of the Metre (May 20, 1 875) 225 

2 Member States of the Metre Convention 231 

3- Members and officers of the CIPM, and Directors of the BIPM from 1 875 to 1 975 233 

4 The base units of the'SI and their origins 238 

5 Worldwide expansion of the Metric System 243 

6. Publications of the Metre Convention Organs 245 

7, Abbreviations used in this volume 247 



VIII 



FROM THE EARLIER SYSTEMS 
OF MEASURES TO THE 
INTERNATIONAL SYSTEM OF UNITS 



J. de Boer 



Numbers and Measures 

On the occasion of the celebration of the centenary of the Convention 
of the Metre* it seems appropriate to review the origins and historical 
developments of unit systems and in particular of the International System 
of Units, one of the most important results of the broad international col- 
laboration that has been realized in the framework of the Convention of the 
Metre. 

The development of such an internationally accepted unit system is 
closely related with the history of science itself. The purely metrological 
aspects of the development of weights and measures and of measuring 
standards in general are of course directly influenced by science and 
technology. But also the logical structure of the system, the symbolical and 
mathematical formalism and the manner in which numerical statements 
are expressed are intimately connected with the status of the mathematical 
sciences at any given moment. Moreover, adequate methods to measure 
and to express results of measurements in a symbolic form are also essen- 
tial for the development of the experimental sciences such as physics, 
chemistry, and technology. There exists an intimate interaction which Cas- 
sirer expressed as follows: "'Physical theories gain their definiteness from 
the mathematical form in which they are expressed. The function of num- 
bering and measuring is indispensable even in order to produce the raw 
material of facts that are to be reproduced and unified in a theory." 

So even a brief review of the history of such a unit system as the Inter- 
national System of Units — related with and deeply rooted as it is in the 
development of modern science and technology — necessarily has to pay at- 
tention also to the symbolism for expressing numbers and numerical state- 
ments and to the whole set of formal symbohc rules which all together con- 
stitute the elements of a sophisticated system of units and which give it its 
central place in modern exact science. 



Editor's note: In the U.S.A. commonly called "Treaty of the Metre." 



1 



Balance of around 5000 B.C.. iduiid in a |ii fliistoric lomli in Na^iada in Efjypt: length cif beam 
= 8. .5 cm (Courtesy Petrie Museum. University College London). 

In most of the early civilizations the economic needs for making quan- 
titative measurements, for instance of areas of land, amounts of food, 
water, and materials, and for establishing reliable time scales and calen- 
dars, led in an early phase to the introduction of systems of counting and 
expressing numbers, and of various measures and measuring systems for 
a great variety of purposes. Obviously we are unable to go here into a 
detailed account of this early history; we have to limit ourselves to a few 
main points which are relevant for our subject. 

Already in the early Egyptian system of measures, mainly of length, 
area, and volume, a decimal system of counting was used, with distinct 
symbols for the numbers 1. 10. 100. and 1000. The decimal system was 
also, though not systematically, used for expressing multiples of their basic 
measures: their basic length unit was the "meh" or cubit; the "khet" is 
equal to 100 cubits. The "sethat." the unit of area of land, is equal to a 
square khet. etc. However, for the submultiples of the cubit no decimal 
fractions were used: thus for instance the "shesap" (or handpalm) and the 
"djeba" (or finger) were equal to 1/6 and 1/24 of a cubit respectively. 

It is well known that the Sumerians and Babylonians used a 
sexagesimal system, which had in fact many advantages because of the 
easy divisibility of the number 60 by 2. 3. 4. 5. 6, 10, 12, etc. The very high 
level of astronomy and advanced status of time-measurement in these early 
Mesopotamic cultures and the influence which this early development had 
in the later development of science have resulted in the absorption of es- 
sential features of this sexagesimal system into western civilization. We 
still divide 1 hour into 60 minutes and 1 minute into 60 seconds and these 



2 



units are so universally used that they had to be maintained as such for use 
with the present International System of Units! 

However, their system of measures did not make systematic use of 
sexagesimal division: thus for instance one "kus" (cubit) was divided into 
30 "shusi" whereas 12 kus made a "gar" (comparable to the pole), which 
was frequently used for land measurements. 

A very important new development appears in the cuneiform texts of 
the Sumerians: their symbol for 60 was the same as that for 1 and the value 
to be attributed to this symbol depends on its position in the number. So 
the Sumerians really introduced positional notation in writing numbers, 
contrary to the Egyptians who repeated the symbols for 1, 10. 100, etc., as 
many times as was needed to symbolize large numbers. This invention of 
positional notation is well known to have been of the utmost importance for 
the simplification of numerical calculations, but it would still take a long 
time before the decimal system of the Egyptians was combined with the 
positional notation. 

What was needed here were separate symbols for the numbers 1 to 9 
and for zero, which were introduced in India in the first centuries, A.D. 
From these Indian symbols originate the Western Arabic figures, from 
which our figures have been derived, as well as the Eastern Arabic figures, 
which have developed into the present Arabic notation. The oldest inscrip- 
tions using a real decimal and positional notation with Indian figures date 
from around A.D. 600. The zero seems to have come into use only a few 
hundred years later. 

The introduction of these figures in Western Europe still gave rise to 
considerable difficulties. In fact. Europe inherited from Rome the 
"Roman" figures with their complex juxtapositional notation and the use 
of the abacus for numerical calculations. The Indian-Arabic figures with 
positional notation for the numbers 1 to 9 and the zero sign, became known 
through the books on Indian calculation from the Arab writer Al-Khwariz- 
mi. which were translated into Latin in the 12th century by an English 
monk. The reaction to the use of Indian-Arabic figures in Western Europe 
was not always favorable: in fact their use instead of the usual Roman 
figures was often forbidden by the banks, which feared confusion. The 
struggle between the "abacists" and the "algorithniicists," supporters of 
the abacus and of Al-Khwarizmi respectively, continued up to the 15th cen- 
tury; but gradually people in Europe became convinced of the superiority 
of the system of Arabic figures with positional notation, which we use at 
present. 

Before leaving this subject, it should be mentioned that a separate ef- 
fort was yet needed to introduce the decimal notation for fractions. Figures 
hke 8 1/4 and 1.37 .3/8 were usually used instead of 8.25 and 137.375. Many 

claims for the invention of the decimal writing of fractions have been 
made — the Chinese used decimal fractions already around A.D. 1200 — but 
it is generally agreed that very much of the credit for its introduction in Eu- 



3 



rope has to jio to Simon Steviii from Leiden who pubhshed in 1585 his 
famous essay "De Thiende" (The Tenth), very soon translated into En^hsh 
and French. In this essay decimal fractions in positional writing were in- 
troduced and the modern calculus with decimal fractions was developed in 
great detail. John Napier, the inventor of the logarithms, was responsible 
for introducing the decimal sign. Another very important contribution of 
Simon Stevin was his request to replace the existing great variety of frac- 
tions and multiples of existing measures by decimal fractions in the mea- 
sures for lengths, surfaces, and capacities as well as in astronomy (angles!) 
and in money systems. This proposal was certainly a very clear example of 
the foresight which he had for the needs of a good measuring system in the 
future. Indeed, the main prerequisites in the field of calculation, which 
were needed for setting up a good system of units, had now been obtained. 

After having gone, very briefly, into the history of numbers — an essen- 
tial element of the precise expression of the results of measurements — we 
now return to the measures themselves. 

In fact, most of the early practice in Europe in making quantitative 
statements in the field of weights and measures was inherited from the 
Romans. Their weights and measures were based on the basic units of 
length and weight, the "pes" or foot and "libra" or pound respectively. The 
unit of capacity, the "amphora," was equal to one cubic pes. But for land 
measurements the square pes was too small; in fact the Romans used the 
"jugerum" which was equal to twice the area of a square on a side of 120 
pedes. In addition a great many other units were introduced which were 
simple fractions and multiples of these units, so that no systematic use of 
decimal multiples and submultiples appears in these Roman weights and 
measures, contrary to their decimal system of counting. Many of these 
Roman weights and measures were taken over in the civilization of 
Western Europe, but the rather feudal structure of the society, developing 
after the breakdown of the Western Roman Empire, led to a large diversity 
of local customs, of weights and measures and rules, which was a source of 
much confusion. Already in 789 Charlemagne had promulgated a decree on 
the unification of measures in all countries under his crown but unfortu- 
nately this attempt disappeared with the empire of Charlemagne. The 
development of a new society, following the growth of important and inde- 
pendent towns in Italy, France, Germany, and other countries starting in 
the 14th century, and the corresponding growth of an economy, based on 
manufacture and money, and on trade relations over land and over sea, was 
a stimulus for the growth of science: mathematics, astronomy, mechanics, 
and the technical sciences. The quantitative aspects of life became more 
and more important and as a consequence weights and measures were also 
looked at more carefully. Several attempts were made in the great king- 
doms of the 15th and 16th centuries to introduce well defined systems of 
weights and measures. 



4 




Averdepois" weight of Edward III. (British Crown Copyright. Science Museum, London.) 



5 



"Pile de Charlemagne"" with its case bearing the inscriplioii ""i'dids Driginal de la Cour des 
Monoyes" (Musee National des Techniques. Paris). 

In France, at the end of the 15th century, the "Pile de Charlemagne" 
defined the "Livre poids du marc" (490 g) and its (nondecimal) subdivi- 
sions; and around 1670 the "Toise du Chatelet" was introduced, one sixth 
of the length of which defined the length of the "Pied du Roi" (32.5 cm), the 
French foot, in terms of which the "pouce," the "ligne" and the "point" 
were defined by successively dividing by twelve. In England Queen 
Elizabeth I introduced at the end of the 16th century the "avoir du poids" 
weight of 1 pound (453 g) divided into 16 ounces and the yard divided into 
3 feet (30.5 cm), each foot being 12 inches. But in spite of these valuable at- 
tempts to unify weights and measures the confusion persisted: in fact even 
the French government never succeeded in imposing the "Parisian" units 
on the whole country, and so in the whole of Europe an infinite variety of 
weights and measures continued to exist. 

Origin of the Metric System 

So it is not surprising that in the course of the 17th and 18th centuries 
not only leading people in government circles, but also scientists who were 
making the first important steps in developing the modern picture of ex- 
perimental sciences, became more and more disturbed by the existing dis- 
order and uncertainty as regards the various weights and measurements, 
which they too had to use to express their experimental results. In 1742 a 



6 



group of scientists made a careful comparison between the so-called "Paris 
measures"' and those used in England at that time, with the result that the 
French "pied" and "livre" were found to be larger than the English "foot" 
and "pound" by 6 and 8 percent respectively. Scientists started to search 
for a suitable universal unit — not bound to any nationality — on which a 
system of measurements, identical in all countries, could be based. Two 
very different propositions were made for the choice of the basic unit of 
length: one being the length of a seconds pendulum and the other being a 
basic length related to the length of an arc of the meridian. The first 
proposal had already been made by the French astronomer Mouton (1670) 
and by Huijghens (1673) and was supported by the Royal Society of Eng- 
land. In France Talleyrand in 1790 made a formal proposal to the Con- 
stituent Assembly in this same direction, but the French Academy of 
Sciences rejected the proposal for the well known reason that the length of 
the seconds pendulum depends on the gravitational acceleration and there- 
fore differs from place to place on the earth. The Academy favored the al- 
ternative proposal and on its recommendation the General Assembly 
adopted in 1791 the principle of a system of weights and measures founded 
entirely on one base unit of length, the "metre, defined to be equal to one 
ten-millionth of the length of the quadrant of the earth meridian. Units of 
area and capacity would be decimal multiples and submultiples of the 
square metre and the cubic metre respectively and the unit of weight (or 
mass) would be the weight (or mass) of a cubic decimetre of water at the 
temperature of maximum density (4 °C).' The system would have to be en- 
tirely decimal, using prefixes like milli (1/1000), centi (1/100), deci (1/10) 
and deca (10), hecto (100) and kilo (1000) to be added to the names of the 
units to indicate submultiples and multiples. Because of its foundation en- 
tirely on the metre this system got the name "Systeme Metrique," the name 
through which the system would gradually spread all over the world. Unfor- 
tunately, however, the English and American governments considered the 
French proposal impracticable and decided to derive their basic unit of 
length on the seconds pendulum, so that the French people had to pursue 
their goal alone. 

Soon after this decision Delambre and Mechain measured the arc of 
the meridian between Dunkerque and Barcelona whereas Lavoisier and 
others made careful measurements of the weight (or mass) of a known 
volume of water. On the basis of these measurements an end standard 
made of sintered platinum representing the metre and a platinum standard 
kilogram were constructed and then deposited as such on June 22, 1799 in 
the Archives de la Republique in Paris. These two standards really would 
be the starting point for the whole development of the present universally 
adopted International System of Units. Already in 1793 Lavoisier said: 



'The Romans had already chosen their unit of capacity, the amphora, such that the amount 
of water filHng the amphora weighed exactly an attic talent. 



573-106 O - 75 - 2 



7 



Metre and Kilogram "of the Archives" (1799) with their cases bearing the inscription "Con- 
forme a la Loi du 18 Germinal an 3. presente le 4 Messidor an 7," and decrees of 1793 and 
1795 instituting the Metric System in France (Photo Archives Nationales, Paris). 

"Never has anything grander and simpler and more coherent in all its parts 
come from the hands of men." 

However — from the formal point of view — it has to be remarked, that 
the final result: the metre and kilogram "des Archives," two basic stan- 
dards for length and weight (or mass) which were legally given the values 
of 1 metre and 1 kilogram respectively, in fact represented a system of 
weights and measures based on two material standards, which in the future 
might easily be found to deviate from their origin: the length of the 
quadrant of the earth meridian and the simple numerical value for density 
of water agreed upon by definition. In fact it was found later than the 
"Metre des Archives" is about 0.2 mm shorter than one ten-millionth of the 
length of the quadrant of the meridian and that the mass of the "Kilo- 
gramme des Archives" is equal to that of 1.000 028 cubic decimetres of 
water — at the maximum density — instead of 1 cubic decimetre exactly.^ 



- This small difference has been the source of long controversy about the ratio of the litre, 
defined as the volume of 1 kg of water at its maximum density, to the cubic decimetre: this 
ratio is given by the same number 1.000 028. In 1964, the litre was finally defined to be exactly 
1 dm^. 



8 



The Metre Convention 



With the initiative of the French people the starting sign had been 
given for a triumphal tour of the metric system all over the world. Already 
in 1820 the system was introduced by law in the Low Countries (Holland, 
Belgium, and Luxembourg). Spain, Colombia, Mexico, Portugal, Italy, and 
many other countries followed. In 1864 the use of metric weights and mea- 
sures concurrently with those of the imperial system was authorized in 
Great Britain and a few years later the metric system was introduced in 
Germany. 

During the world exhibition of Paris in 1867 a great many scientists, 
impressed by the tremendous industrial development in the world, created 
a Committee for Weights and Measures and for Money, with the special 
task of creating more uniformity in the world. Following this valuable initia- 
tive the French government in 1869 invited numerous countries to send 
delegates to Paris for an "International Commission for the Metre." A total 
of 24 countries appointed delegates and the meetings started in August 
1872. The great majority of those present at the meeting felt that the metre 
and kilogram which were conserved in the "Archives de Paris ' should be 
the reference for new prototypes and for various copies to be constructed 
and distributed among the participating countries. 

Unfortunately the work was interrupted by the Franco-Prussian war 
but in 1872 the same Commission, then consisting of delegates represent- 
ing 30 countries, met again and confirmed its previous decision to con- 
struct new prototypes of the metre and the kilogram and to provide a large 
number of copies, all made from one single melt of a special platinum-iridi- 
um alloy with 10 percent iridium. The standards of the metre should be 
line-standards with an X-shaped cross section. The values of the new proto- 
types should be based on the metre and the kilogram in the "Archives." 

On the 1st of March 1875 the French Government convened the 
"Conference Diplomatique du Metre" to which 20 countries had sent 
government representatives and scientists who were authorized to sign for 
their governments. These delegates approved the proposals made by the 
Committee, so that finally on the 20th of May 1875 the "Convention du 
Metre" could be signed officially. 

The newly established "Comite International des Poids et Mesures" 
concentrated on the preparations for the construction of the prototypes and 
the various copies of the metre and the kilogram. Many very serious dif- 
ficulties had to be overcome and it was a real scientific accomplishment of 
the first order when in 1899 at the first "Conference Generale des Poids et 
Mesures" the national prototypes could be distributed and approval given 
to the two prototypes for the metre and the kilogram which from then on 
were considered to form the basis for the metric system. These prototypes 
were to be conserved in the "Bureau International des Poids et Mesures," 
which should be the central laboratory for future international comparisons 



9 



and which should be the international center for the propagation of the 
metric system. The International Bureau should work under the direction 
and exclusive supervision of the International Committee which itself is 
subordinated to the General Conference. 

We will not follow the history of the International Bureau of Weights 
and Measures and its further expansion together with the governing 
bodies: the International Committee and the various Consultative Commit- 
tees. This will be dealt with elsewhere in the present volume. Our aim is to 
review briefly the development of the scie;ntific ideas about units and how 
they have to be related and combined into a unit system. 

The Concept of a Unit System 

The two or three centuries preceding the signing of the metre conven- 
tion had been a period of tremendous scientific development in which the 
role of physics as the most advanced experimental science had become 
more and more pronounced: physics had developed into a real science of 
measurements, in which the concept of "physical quantities" is in- 
troduced; these are mathematical entities, such as mass, force, energy, 
etc., connected with and describing the physical phenomena. They are 
defined in terms of actual measurements and their introduction leads to a 
description in terms of mathematical relations between these physical 
quantities, which can be looked upon as definitions or as physical laws, 
although this distinction is generally difficult to make. 

According to Maxwell every physical quantity can be expressed as the 
product of a pure number and a unit, where the unit is a selected reference 
quantity in terms of which all quantities of the same kind can be expressed. 
The ratio of the quantity to the corresponding unit, which is a number, is 
usually referred to as the numerical value of the quantity expressed in that 
particular unit. The unit as introduced here thus has the same kind of ab- 
stract mathematical character as the corresponding physical quantity it- 
self. Such abstract units should therefore not be confused with their ex- 
plicit physical realizations, which are usually called measurement units or 
standards. 

Physics had become the prototype of an exact science. Obviously the 
choice and the definition of the units for the various physical quantities and 
the way they are integrated into this mathematical description as a "unit 
system" are extremely important. The experimental and metrological 
aspects of physics and the various related engineering sciences require an 
ever increasing experimental accuracy, which leads to a continuous need 
to improve the precision of the measuring standards representing the vari- 
ous units. On the other hand the theoretical and mathematical aspects of 
the physical sciences require the units to constitute a logical system, which 
itself is an integral part of the whole mathematical formalism through 



10 



which the various relations between physical quantities and the laws of 
physics are expressed. We briefly sketch some important steps which 
seem to be essential in the long and often very curved road, which runs 
from the beginnin<i of the French Metric System up to the present more so- 
phisticated International System of Units. 

In the second half of the last century, the British Association for the 
Advancement of Science (B.A.A.S.) played an important role in developing 
the concepts relating to unit systems. In particular the Standards Commit- 
tee has been a center of very fruitful cooperation of a great many famous 
scientists of that time, among whom Maxwell, in particular, should be men- 
tioned. This Standards Committee studied around 1860 the best choice for 
the units corresponding to the various physical quantities such as electric 
charge, current, resistance, capacitance, and potential, which had been in- 
troduced in the theory of electricity. The Committee made clear that when 
a unit corresponding to a particular physical quantity has to be defined, 
there are always two questions to be answered: one should first determine 
what would be the most convenient unit and then second, what would be 
the best form and material for the standard physically representing that 
unit. 

Although in principle one would be able to choose a unit and a cor- 
responding standard for every kind of quantity it would be very inefficient 
to choose all the units independently. We have seen that already at a very 
early stage people felt that, for instance, the unit of area should be chosen 
to be the square of the unit of length. Only because of reasons of con- 
venience, multiples or elementary fractions of this more systematic choice 
often came into use. In the metric system the logical choice for the unit of 
velocity is the metre per second, and the kilometre per hour which is so 
widely used at present is not "coherent" with this system. 



The CGS-Unit System 

The B.A.A.S. Standards Committee stressed the need for a coherent 
unit system which is built up systematically on a certain number of "funda- 
mental" units — or base units as they are called now. The three base units 
for mechanics were chosen to be the centimetre, the gram, and the second 
of mean solar time, the centimetre being chosen instead of the metre 
because in fact one cubic centimetre — and not one cubic metre — of water 
had a mass of approximately one unit of mass (or gram) at the temperature 
of maximum density of water. The corresponding base standards of length 
and mass were accepted to be those conserved in Paris, whereas the defini- 
tion of the time scale was left to the astronomers. This was the birth of the 
CGS-systeni, the first system of units conceived as such and still very much 
in use in physics. 



11 



The development of physics into an exact science governed by a 
mathematical system of equations, thus also has its implications for the 
units. Only a Hmited set can be arbitrarily chosen and once the choice of 
these base units has been made, the whole system of units can be built up 
systematically. 

One number of base units on which the physics of mechanical 
phenomena could be based appeared to be three, and the actual choice of 
the three fundamental quantities length, time, and mass — on the units of 
which the CGS-system was based — agreed with what intuitively had al- 
ready been the selection for centuries. Often such a system is called a 
three-dimensional system, the number three referring here to the number 
of independent base units or quantities on which the system was based. 

Once the three base units are decided upon, the requirement of 
coherence is sufficient to define all the other units, at present called 
derived units, in contrast to the base units. Thus for instance the physical 
quantity "velocity" is defined as distance travelled per unit time and as a 
consequence the "coherent" unit is defined to be the centimetre per 
second (cm/s), the physical quantity "momentum" is defined as mass times 
velocity so that the coherent unit is the gram centimetre per second (g • 
cm/s), "force" is defined as increase of momentum per unit time with the 
unit (g • cm/s)/s or g • cm/s- and "work" is defined as force times length of 
path with the unit (g • cm/s-) • cm or g • cm-/s-. In this way for every quanti- 
ty, following its definition in terms of other quantities, the corresponding 
unit can be coherently defined. Any coherent unit system built up in this 
way is based on the system of equations which relate the various physical 
quantities. 

New problems arose when electrical phenomena had to be taken into 
account. Already in 1832 Gauss — in his famous publication "The intensity 
of the earth's magnetic force reduced to absolute measure" — stressed the 
need to replace geomagnetic measurements with a magnetic needle by 
"absolute" measurements in terms of mechanical units of force. For that 
purpose Gauss introduced an "absolute" unit system for the electrical 
units based on the millimetre, the milligram, and the second. Gauss was 
supported by Weber who extended his work to other electrical measure- 
ments. In England William Thomson, later Lord Kelvin, made similar mea- 
surements in the early fifties — measurements needed for telecommunica- 
tion—in terms of the British mechanical units. In 1863 Maxwell wrote: 
"The phenomena by which electricity is known to us, are of a mechanical 
kind and therefore they must be measured by mechanical units or stan- 
dards." The B.A.A.S. Standards Committee recommended following the 
same scheme and in particular extending the CGS-unit system by defining 
appropriate units for all electric quantities by just following the equations, 
developed by Faraday, Thomson, Maxwell. Weber, and many others, ex- 
pressing them in terms of mechanical quantities length, time, force, and 
work. The units so obtained were called "absolute" in the sense of 



12 



"coherent," i.e., they were not arbitrarily chosen but were simply the con- 
sequence of the system of equations by which the electrical and magnetic 
phenomena are represented. Unfortunately the electrical and magnetic 
phenomena could actually be described by two — mutually incompati- 
ble—systems of equations, depending on whether one started from the in- 
verse-square distance force law between two magnetic poles or from that 
between two electric charges. For each of these two systems of equations 
Weber defined in 1851 a coherent "absolute" unit system and he called the 
two "absolute" CGS-unit systems: the electromagnetic and the electro- 
static systems. The electromagnetic CGS-unit of electric resistance thus 
turned out to be one centimetre per second and already in 1851 Weber had 
performed beautiful experiments to determine the electric resistance of a 
wire in this "absolute measure." 

The Standards Committee adopted in 1863 a method proposed by W. 
Thomson for such an "absolute" resistance measurement, with which 
method successful experiments were performed by Maxwell, Stewart, and 
Jenkin. With these measurements of the electric resistance a standard re- 
sistance in the form of a resistance coil could be prepared, the value of 
which in electromagnetic CGS-units would be obtainable with a sufficient 
precision of about 1 in 10,000. Once this electric resistance standard would 
be available the measurement of all other electric quantities such as elec- 
tric current and electromotive force in terms of electromagnetic CGS-units 
was considered to offer no more serious difficulties. 



Practical Electric Units 

However, the size of the electromagnetic CGS-units proved to be 
much too small, which was the reason that the B.A.A.S. recommended the 
use of certain "practical" units, i.e., the ohm for resistance and the volt for 
electromotive force, which were equal to 10"' and 10** times the correspond- 
ing electromagnetic CGS-units respectively. The First International Elec- 
trical Congress approved this decision in Paris in 1881 and even introduced 
one more practical unit: the ampere for electric current, which was equal 
to one tenth of the corresponding electromagnetic CGS-unit. Later on the 
coulomb for electric charge and the farad for capacitance and several 
others were added. 

This set of practical units actually also formed a "system" in the sense 
that they constituted a system, coherent with the system of equations con- 
necting the electrical quantities with each other, but not with those in 
which mechanical quantities Uke force or work occurred. For instance the 
practical units of work, the volt-ampere-second, called joule, was equal to 
10^ CGS-units of work. The introduction of these units, needed for practical 
purposes, thus spoiled the beautiful coherence of the original electromag- 



13 



netic CGS system: only a limited coherence of the electric units among 
themselves was left. 

There was, however, another very disturbing development: so far the 
definitions of the practical units were still "absolute" definitions in the 
sense that they were still given — with integral powers of ten — in terms of 
the (absolute) electromagnetic CGS-system. However, the material stan- 
dards of the ohm (a mercury column), the volt (the Weston cell) and the am- 
pere (silver voltameter), which were used for practical purposes as secon- 
dary standards, started to live their own life: at the International Electrical 
Congress in 1881 and more clearly at that in Chicago in 1893, the ohm, the 
volt, and the ampere were "legally" defined in terms of these material stan- 
dards. Although the numerical values of these material standards ex- 
pressed in electromagnetic CGS-units did not deviate very much from the 
integral powers of ten, it was nevertheless clear that the principle of this 
decision to define the electric units in terms of independent material stan- 
dards, was quite contrary to the coherence principle used so far by the 
B.A.A.S. in their "absolute" definitions. However, the International Elec- 
trical Congress in London confirmed these new developments in 1908 and 
even adopted for legislation purposes and for metrology a complete system 
of these so-called "international" electric units based on the material stan- 
dards of the ohm and the ampere. It would still take more than 25 years be- 
fore this decision could be reversed, but we first have to pay attention to 
various developments which took place in the description of electrical 
phenomena. 

The Giorgi Proposal 

In the beginning of this century very important new ideas came up 
about the theoretical presentation of the electrical and magnetic 
phenomena and the construction of its unit system, which ultimately would 
lead to a new choice for a coherent unit system covering the whole field of 
electrical, magnetic, and mechanical phenomena. 

Already in 1901 Giorgi remarked that the electric unit of work, the 
joule or volt-ampere-second, which is equal to 10"^ CGS-units of work or 10^ 
g • cm'-/s-, is in fact equal to 1 MKS-unit of work or 1 kg • m-/s-. However, 
simply replacing everywhere the centimetre and the gram by the metre and 
the kilogram in the "absolute" definitions of the electric units does not give 
the practical units because, for instance, the ohm which was defined to be 
10-' electromagnetic CGS-units or 10-' cm/s, is equal to 10' m/s and not to 1 
m/s. 

Giorgi showed that this difficulty could be solved by increasing the 
number of fundamental units or base units on which the unit system for 
mechanics, electricity, and magnetism should be based from three to four 
base units: the metre, the kilogram, and the second of the MKS system, 

r4 



together with one base unit of electrical nature, for instance the ampere or 
the ohm. But the requirement of coherence of the unit system with the 
system of equations relating the various physical quantities then makes it 
necessary also to add to the three base quantities length, time, and mass, 
a fourth base quantity of electrical nature. This means that the electric 
quantities should no longer be defined in terms of the three "mechanical" 
quantities length, time, and mass exclusively — typical of Maxwell's formu- 
lation of the electromagnetic theory — but that in the force law for the mag- 
netic interaction, which Maxwell had considered to be the starting point for 
the definition of the magnetic and electric quantities and their electromag- 
netic units, a constant of proportionality, the vacuum permeability, now 
had to be introduced. The value of this constant followed from the indepen- 
dent choice of the electric units to be 10"' MKS-units of force per ampere 
squared. 

It would take some time for the ideas of Giorgi to find acceptance 
among physicists and in electrical technology. The original Maxwell formu- 
lation of the theory, based on the mechanical quantities alone, found — and 
even at present still has — its active supporters. Still there was much intui- 
tive logic in the request to increase the number of base quantities by one in 
going from mechanics to the description of the electrical phenomena. One 
might say that basic for any theory in physics are the base quantities for 
length and time. Characteristic for the mechanical dynamics is the concept 
of mass, which connects force and acceleration and which determines also 
the gravitational interaction. In electricity a similar quantity — of the same 
kind of fundamental nature — is the quantity electric charge or current. As 
long as this quantity is not shown to be of mechanical nature it plays in 
electricity a role similar to that of mass in mechanics, so that the total 
number of base quantities should increase to four. Consequently also the 
number of units on which the coherent unit system should be based, should 
be four. 

Another indication of the insufficiency of the Maxwell presentation of 
all electric quantities and units in terms of mechanical ones alone was the 
fact that the formal unit expressions often carried fractional exponents, 
e.g., the electromagnetic CGS-unit of electric current: cm^'- ■ g"-/s, or the 
occurrence of rather strange unit expressions like the cm/s for electric re- 
sistance. These are all clear indications that the chosen number of base 
quantities and units is too small. The only conclusion could be that in the 
future the equations of Maxwell ought to be rewritten in four-dimensional 
form, i.e., with four base quantities — including one of electrical na- 
ture—such that a coherent unit system would also be founded on four base 
units, three of mechanical and one of electrical nature, in agreement with 
the 1901 proposal of Giorgi. 

In addition scientists became more and more convinced that it would 
be logical to introduce one more change in Maxwell's set of equations for 
electricity, i.e., to introduce numerical factors 477 in various places, where 



15 



they would logically occur, and to drop them from other places (so-called 
"rationalization"). As a result of the coherence of the unit system, this does 
not change the formal expressions for the units, but it does change the size 
of some of the corresponding standards. In fact it also modifies the value of 
the vacuum permeability into • 10 " MKS-units of force per ampere 
squared. So at present the four-dimensional set of equations for electricity 
is always written in the "rationalized" form. 

After long discussions in various international organizations the Inter- 
national Electrotechnical Commission, at its meeting in Scheveningen in 
1935, adopted the Giorgi proposal, leaving still open, however, the choice 
of the fourth quantity and unit of electrical nature on which the system 
should be based. 

In this connection it is important to note that Giorgi, supported by vari- 
ous other scientists, was in fact in favor of choosing this fourth electric unit 
to be the international ohm, defined by an independent primary standard. 
Others, however, favored one of the practical units defined as mentioned 
above on an "absolute" basis. The choice was left open in order to obtain 
the opinion of the International Committee for Weights and Measures and 
that of the S.U.N. Commission for Symbols, Units and Nomenclature of the 
International Union of Pure and Applied Physics — presided over by Sir 
Richard Glazebrook — which commission in the past had already made im- 
portant contributions to the formulation of the new ideas. 

What made the discussions and decisions so difficult at that time, 
were the conceptionally very different points of view which various 
scientists had about the philosophy of setting up a unit system: on one hand 
there was the metrological point of view, which was trying to define a mea- 
suring standard for every quantity and to establish primary standards for 
a certain set of base units which were metrologically independent. From 
this metrological point of view the original Giorgi proposal with an indepen- 
dent base unit for resistance represented by a primary standard, was the 
simplest solution. Defining electric quantities by giving the permeability of 
vacuum the numerical value 477 X 10"' seemed to be strange to the usual 
metrological procedures. It appears to be similar to defining the unit of 
mass in terms of the metre by giving the density of water, at the tempera- 
ture of maximum density, the value of 10^ kg/m^ by definition, a principle 
which was originally aimed at in the metric system, but which was given up 
later in view of the metrological praxis, which required standards for both 
length and mass. 

On the other hand there was the systematic point of view, which looked 
primarily at the algebraic rules, which any unit system — coherent with a 
system of equations between physical quantities — has to satisfy. This 
required a system with a fourth independent electric quantity and unit — in- 
dependent from the systematic or algebraic point of view. The reasons are 
then essentially the arguments, partly theoretical or algebraic and partly 



16 



more philosophical, which were given above in favor of the four-dimen- 
sional system. 

In the case under consideration the systematic point of view prevailed. 
The International Committee decided in 1935 that: 

(1) the permeability of vacuum, in the rationalized form of writing the 
equations, was defined to be 477 X 10 newton per ampere squared, where 
the newton was introduced as a new name for the MKS-unit of force. 

(2) a definition of the ampere in terms of the force between two parallel 
conductors was considered to be the most appropriate basis for deriving all 
the other practical electric units. 

However, for the transition from the abandoned "international" units 
to the "absolutely" defined electric units one now had to make available 
accurate values for the conversion factors. The final decision on these con- 
version factors was interrupted by World War II. However, in 1946 the In- 
ternational Committee, authorized by the General Conference in 1933, for- 
mally confirmed its previous decisions, the date for the introduction of the 
"absolute" practical electric units being decided to be January 1, 1948. 

The International System of Units 

The general tendency, existing after World War II, to further intensify 
international collaboration and to review the existing situation with the aim 
of promoting everything which would advance better international un- 
derstanding in particular in science and technology and in international in- 
dustrial and trade relations, had also a definite influence on the develop- 
ment of a generally accepted international unit system. There still existed 
a large diversity of systems: in France the metre-tonne-seconde (M.T.S.) 
system had been introduced legally in 1919; in technical circles a technical 
metric system, the metre-kilogram-force-second system, was generally 
used with the confusing name "kilogram" for a base unit of force instead of 
mass; physicists used the COS system; and in England and the U.S.A. 
similar systems based on the foot, pound, and second had been used for 
centuries. 

The International Union of Pure and Applied Physics and its S.U.N. 
Commission for Symbols, Units and Nomenclature had expressed the need 
for the international adoption of an "international practical system of 
units" for international communication, to be based on the metre, the 
second, the kilogram and an electric unit of the absolute practical system. 
A similar request was made by the French government. This resulted in an 
international inquiry made by the International Committee — on the 
request of the 9th General Conference in 1948 — in scientific and technical 
circles and in institutions charged with education and teaching. On the 
basis of the information obtained, the 10th General Conference decided in 
1954 that such an international practical system should be based on six 



17 



base units, i.e., the metre, kilogram, second, ampere, kelvin,'' and candela. 
The choice of the first set of four base units agreed with the MKSA-system 
already approved in 1948. The introduction of the kelvin and the candela 
may require some special attention. 

So far the physical phenomena for which a unit system was designed 
were of purely mechanical, electrical or magnetic nature, such that their 
description in terms of physical quantities could be based entirely on the 
four base quantities: length, time, mass, and electric current. However, for 
the description of thermal phenomena a new base quantity, the ther- 
modynamic temperature, has to be introduced both for systematic and for 
metrological reasons. The ratio of the thermodynamic temperatures of two 
systems is determined by thermodynamics — using a Carnot cycle — in 
terms of the ratio of two amounts of heat (or energy). In agreement with the 
procedure followed in defining standards for other base quantities it is then 
sufficient to attach — by definition — a certain numerical value to the ther- 
modynamic temperature of one particular physical state. In 1948 the 
General Conference had selected this physical state to be the triple point 
of water and in 1954 the corresponding thermodynamic temperature was 
defined to be 273.16 kelvins^. 

If we now turn to the description of the phenomena of light it appears 
that here three base quantities are sufficient: length and time and one 
physical quantity of luminous origin for which the luminous intensity has 
been chosen. The candela, the unit of luminous intensity, is then defined as 
the luminous intensity in the perpendicular direction of a particular area of 
a blackbody at a certain specified temperature. This definition was ap- 
proved by the General Conference in 1948 and was put in its final form in 
1968. 

In 1960 the 11th General Conference gave the name "International 
System of Units" to the unit system based on the six base quantities and 
units already introduced in 1954. For all other quantities the corresponding 
derived units can be expressed in the base units, although in many cases 
special symbols are given. Only for the two quantities plane angle and solid 
angle was it left undecided by the General Conference — in view of the 
many different existing opinions in this field — whether these have to be 
considered as base quantities or as derived quantities. The corresponding 
units, the radian and steradian, were placed in a separate group with the 
name "supplementary units" and may be regarded either as base units or 
as derived units. The base units and the derived units together with these 
supplementary units, were called SI Units, where "SI" is the generally 
adopted abbreviation for International System. This set of SI units forms 
a coherent system of units in the sense explained in the previous sections 
of this article: the system is directly related to the whole set of algebraic 
equations on which physics, chemistry, and technology at present is based. 



Still called the degree Kelvin at that time. 



18 



The system includes also a set of symbols for prefixes to be used to form 
decimal multiples and submultiples of the SI units. 

It has already been stated that the whole structure of the International 
System of Units is intimately related with, and forms part of, the whole 
mathematical description of the physical phenomena, on which modern 
sciences are built. But then it must also be understood that such a system 
of units cannot be adopted for eternity: as science is developing, so is the 
International System of Units. One must expect that from time to time 
necessary improvements or changes have to be introduced in order to keep 
the system up to date with developing science. 

When the system was adopted it was already evident, for instance, 
that the quantity mass, although it may be an appropriate concept in 
mechanics, is entirely unsuitable for use in chemistry where the molecular 
structure and in particular the number of molecules in a system is much 
more relevant than its total mass. For that reason the concept "amount of 
substance" has been introduced in chemistry as a useful and necessary 
base quantity with the base unit mole, which by definition is the amount of 
substance of 12 grams of carbon-12. In 1971 the General Conference added 
this base quantity and its unit as such to the International System of Units. 

The International System has had a considerable impact on science 
and technology, in the international relations between countries and civil 
hfe: in education and teaching at the primary, secondary, and university 
levels. Of course the gradual development of this system has not 
eliminated at once all other systems, neither has the great diversity of units 
not fitting into the system suddenly disappeared. Some of these units had 
to be retained for general use, but others have to disappear in the course of 
time. General rules and recommendations have been given in the brochure 
"The International System of Units" published by the International Bureau 
and edited for the International Committee by its Consultative Committee 
for Units. In this brochure one finds the full definitions of the seven base 
units of the International System together with further explanations con- 
cerning their practical realization. The logical structure of the International 
System — with its SI units and their decimal multiples and submultiples — is 
presented together with various rules adopted by the General Conference 
about the symbolic representation, and additional recommendations of the 
International Organization for Standardization (ISO). Both of these are es- 
sential for the incorporation of the International System into the whole 
mathematical structure which describes our present day knowledge in the 
field of the exact sciences and technology. I would like to close this con- 
tribution by expressing the hope that the very fruitful cooperation which 
exists between various international organizations will continue with the 
aim of further improving the International System as an efficient tool in the 
field of science and technology and as an essential hnk between the peo- 
ples in a growing world of ever increasing complexity. 



19 




Metric System medal struck in 1840 after a 1799 design. 



20 



CHAPTER I 



HISTORICAL INTRODUCTION 



THE METRE CONVENTION AND ITS ORGANS 



A century has passed since the Diplomatic Conference on the Metre 
was convened in Paris on March 1, 1875. at the invitation of the French 
Government [1]. At the closing session of that Conference, May 20, 1875, 
the plenipotentiaries of 17 of the 20 countries represented signed the treaty 
known by the name. Convention of the Metre. This Convention and its ap- 
pended Regulations sanctioned the birth of the International Bureau of 
Weights and Measures (BIPM),^ a scientific and permanent agency sup- 
ported at the common expense of the signatory countries; its location was 
set in France, the cradle of the Metric System. The BIPM was placed 
under the authority of a diplomatic conference, the General Conference on 
Weights and Measures (CGPM), and of a committee of scientific experts, 
the International Committee for Weights and Measures (CIPM). This agen- 
cy has for its goal the assurance of the "international unification and 
development of the Metric System." 

The BIPM must, for its part, "establish new metric standards, con- 
serve the international prototypes, and carry out the comparisons necessa- 
ry to assure the uniformity of measures throughout the world." 

The accomplishments prior to the fiftieth anniversary of the creation 
of the BIPM have been described in the volume on that occasion pubhshed 
in 1927 [2]; the origins of the Metric System and of the Convention of the 
Metre, and the history of the Pavilion de Breteuil have an important place 
therein along with the work of the BIPM during the first half century of its 
existence. We shall repeat only the main topics of this past. 

The Metric System was born from the desire to put an end to the chaos 
which reigned in France in the field of measurements (decree of May 8, 
1790). Its founders, however, immediately set themselves a more noble 
aim: to base the measures of the new system on a "universal natural unit" 
which belonged to no one and which could be adopted by all countries 

' Appendix 7 gives the list and meaning of the abbreviations used in this book. 



21 



I 




T 

I 



without problems of national pride. Their choice thus fell on a decimal 
system whose unit of length, the metre, was to be the ten-milhonth part of 
a quarter of the terrestrial meridian, and the unit of mass to be that of a 
cubic decimetre of water. 

This new system was legalized in France on April 7, 1795; the law of 
December 10, 1799, fixed the values of the metre and kilogram by adopting 
the prototype platinum standards known by the names Metre of the 
Archives and Kilogram of the Archives. 

After slow and difficult beginnings, hobbled by contradictory deci- 
sions (1800, 1812, 1816), the law of July 4, 1837, finally made the Metric 
System compulsory in France starting on January 1 , 1840. 

Gradually learned of in foreign countries, appreciated for its simplici- 
ty, its logical structure and universal applicability, the Metric System 
began to spread through Europe and the world. On the occasion of interna- 
tional expositions held between 1851 and 1867, "when man found himself in 
the presence of the immense variety of products sent from all parts of the 
world, and whose values as well as quantities were described in all kinds of 
measurement standards," the need for unification struck all clearsighted 
minds. A "Committee for weights, measures, and currencies." set up on 
the occasion of the 1867 Paris Exposition, announced itself in favor of 
universal adoption of the Metric System. 

The momentum of opinion was launched and events rushed forward 
after the resolutions and recommendations adopted between 1867 and 1869 
by the International Association for Geodesy, the Bureau of Longitude 
(Paris), and the Academies of Science of Saint Petersburg and Paris. The 
International Commission of the Metre (1870, 1872) took the first practical 




Casting the platinum n idium alloy called "1874 Alloy," at the Paris Conservatory of Arts and 
Crafts. (Ulllustration. May 16. 1874). 



573-106 0-75-3 



23 



steps toward the internationalization of the Metric System. The permanent 
working committees and the French Section of this Commission con- 
structed new metric standards, derived from the original standards of the 
Archives, which were to be distributed throughout the world. 

All the preparatory tasks and dehberations culminated in 1875 in the 
signing of the Convention of the Metre (app. 1, p. 225) and in the founding 
of the International Bureau of Weights and Measures. 

* 



Since 1875, the organs of the Metre Convention have not been sub- 
jected to change. However, by reason of the increasing complexity of scien- 
tific questions related to metrology, the CIPM established several Con- 
sultative Committees, starting in 1927. The relations among these organs, 
the member States, the speciahzed international organizations, and the na- 
tional laboratories are shown below. 



Consultative 
Committees 



Working 
groups 



Convention of the Metre 
1875 



General Conference 
on Weights and Measures 
(CGPM) 



International Committee 
for Weights and Measures 
(CIPM) 



International Bureau 
of Weights and Measures 
(BIPM) 



Diplomatic 
treaty 



overnments and 
Member States 



^ Speciolized 
-*-\ international 
bodies 



Notional 
I aboratori es 



The Metre Cdnveiition Organs. In 1975. there are seven Consultative Committees: Electrici- 
ty, Photometry and Radiometry. Thermometry, Definition of the Metre, Definition of the 
Second. lonizinj; Radiation, Units. 



24 



The General Conference on Weights and Measures, an intergovern- 
mental conference comprising delegates of member States of the Metre 
Convention,' is the supreme authority which controls the administration of 
the BIPM; it has for its primary mission: 

— to discuss and initiate the necessary measures to assure the 
propagation and development of the International System of Units 
(SI), the modern form of the Metric System; 

— to ratify the results of new fundamental metrological determina- 
tions and to adopt various scientific resolutions of international im- 
portance; 

— to adopt important decisions concerning the organization and 
development of the BIPM. 

From 1889 to 1971, the CGPM met 14 times. The 15th CGPM coin- 
cides with the centennial of the Convention of the Metre. 

The International Committee for Weights and Measures is charged 
with preparing and executing the decisions of the CGPM. It directly super- 
vises the operation of the BIPM and oversees its work. 

Originally composed of 14 members, a number raised to 18 in 1921, the 
CIPM assembles men of science and eminent metrologists of all different 
nationalities ( app. 3, p. 233). Elected by the CGPM, these members sit in 
the CIPM in a personal capacity and they are not in any way official 
representatives of their countries. The CIPM met for the first time in April 
1875; it held its 63d meeting in 1974, these meetings having been annual or 
biennial at various times. Between meetings of the CIPM, its executive 
committee — comprising a president, a vice-president (position created in 
1954), and a secretary — examine current business, keep the CIPM in- 
formed on important questions, and prepare the meetings. The director of 
the BIPM participates ex officio in the meetings of the CIPM and in the 
meetings of its executive committee. 

Each of the Consultative Commi?iees — occasionally helped by "Work- 
ing Groups" — assembles a small number of representatives of the best 
laboratories in the research and measurements peculiar to a particular 
field of metrology. 

These Consultative Committees, currently seven in number, have the 
mission of advising the CIPM on questions of a scientific nature which it 
submits to their examination: orientation of the work of the BIPM, coor- 
dination of this work with that of the national metrological laboratories, or- 
ganization and promotion of international undertakings, decisions which 
the CIPM is led to take directly or to submit to approval by the CGPM. 



- As of January 1, 1975, 43 States were members of this Convention (see app. 2, p. 231, for the 
list of these States and the dates of accession). 



25 



The International Bureau of Weights and Measures, organ for execut- 
ing the decisions of the CGPM and the CIPM, is a permanent laboratory 
and the world center of scientific metrology whose progress, particularly 
spectacular in our time, is intimately linked to the development of scien- 
tific discoveries, industrial technology, and international comparisons. 

The primary mission of the BIPM is: 

— to establish the basic standards and scales of the principal physi- 
cal quantities, and to maintain international prototypes; 

— to carry out comparisons of national and international standards; 

— to assure coordination of the corresponding techniques of mea- 
surement; 

— to carry out and coordinate relative determinations of fundamen- 
tal physical constants. 

Functioning of the BIPM is assured by an annual appropriation voted 
by the CGPM. Since 1960, this appropriation has been divided among the 
member States of the Metre Convention according to a scale based on the 
factors used by the United Nations; the contributions of the States can not, 
however, be greater than 10 percent, nor less than 0.5 percent, of the total 
appropriation. From an amount of 100 000 gold francs in 1878, the annual 
budget of the BIPM is now some 4 180 000 gold francs for 1975. 

The BIPM has a staff which can be of all nationalities; its director, 
named by the CIPM, must be of a nationality different from those of the 
CIPM officers. This staff, scientific, administrative, technical, and service, 
did not surpass some 10 persons formerly: it consists of some 50 persons in 
1975. 

Like any international organization, the BIPM has, at certain times in 
its existence, known financial difficulties; these have been overcome, 
thanks mainly to subsidies and various gifts, and to generous offers of 
materials and scientific instruments. The periods of the two world wars 
were particularly difficult, but very fortunately the BIPM was able to sur- 
vive them with neither the international metric prototypes nor the measur- 
ing apparatus suffering any damage. 

A neutral and autonomous organ, the BIPM is not dependent on any of 
the existing intergovernmental organizations'' and is not affiliated with any 
international union or association. It has been recognized in France as an 
establishment of public usefulness by the decree of October 28, 1876. On 
April 25, 1969, an Accord was concluded between the French Government 
and the CIPM relative to the grounds of the BIPM and to its privileges and 
immunities in French territory (Decree No. 70-820 of September 9, 1970). 



'Agreements on information and mutual relations have, however, been concluded with the 
United Nations Educational. Scientific and Cultural Organization (UNESCO) (1948), the In- 
ternational Agency for Atomic Energy (1961, 1967), the European Atomic Community 
(EURATOM) growing out of the Commission of the European Communities (1965, 1967), and 
the International Bureau of Legal Metrology (1970). 

26 



I 




Overall plan of the Pavilion de Bieteuil and the lahoratm ies nf ihe International Bureau of 
Weights and Measures in 1975. A: Pavilion de Breleuil; B: lahoratories (1878); C: 
extension of laboratories (1929); D.E; laboratories for ionizing radiations (1964). 

These grounds are situated in the Park of Saint-Cloud, near Paris. The 
French Government graciously placed at the disposal of the CIPM, April 
22, 1876, an estate of 25 153 m- in area,^ where is found the Pavilion de 
Breteuil— name under which the BIPM is also known worldwide. 

The Pavilion de Breteuil proper is a building with a historic past; built 
in 1743 on the site of the former Trianon of Saint-Cloud (17th century) it 
was greatly damaged in 1870-1871. The CIPM restored it and constructed 
a new building (1878) for the laboratories; extension of the activities of the 
BIPM required enlarging the first laboratories in 1929 and the construction 
of new buildings in 1964. 

* 

Such are, briefly summarized, the history and essential characteristics 
of the different organs born of the Metre Convention. In close collaboration 
with the principal national metrology laboratories, these organs have for a 
century unflinchingly fulfilled the mission assigned to them in 1875; their 
permanence reflects that of the Metric System, which will itself soon 
celebrate its bicentennial. 



^ Two extensions have increased this area to 43 517 m'-. 



27 



Tlie Pavilion de Breteuil. then called Pavilion d'ltalie. at the beginninj; of the 19th century. 
(Lavis de Langlace. 1807. Manufacture Nationale de Porcelaine de Sevres). 




The Pavilion de Breteuil, seat of the International Bureau of Weights and Measures (geo- 
graphical coordinates: 48° 50' N, 2° 13' E, altitude 66 metres), on the right: offices, con- 
ference room: on the left: laboratories built in 1878 and in 1929 (the laboratories built in 
1964, located at the rear on both sides of the central lane, are not visible in this photograph). 



28 



A Century of Metrology^ 



1875-1925 

The initial mission of the BIPM was to participate in the preparation 
and determination of the values of the new metric prototypes of platinum- 
iridium destined to be the international and national prototypes. The 
results of this important task [3] were presented to the 1st CGPM (Sep- 
tember 1889); the CGPM ratified the definitions of the units of length and 
mass based on the international Metre and Kilogram*^ as well as the equali- 
ty of some 30 Metres and 40 Kilograms which were distributed by lot 
among the States. 

At the time of founding the BIPM, it was thought that after these first 
basic determinations, its activity would be reduced to periodic verification 
of the national standards. 

It was very quickly seen that this activity implied numerous per- 
manent auxihary studies. It is in fact necessary to be able to determine the 
submultiples and multiples of the units with precision, if only to evaluate 
accurately the differences among the standards to be verified. It is also 
necessary to study the phenomena which affect the measurements, for ex- 
ample, dilatation in the case of length measurements, or air pressure in the 
case of mass measurements; this requires the measurement of numerous 
physical quantities: temperature, volume, density, pressure, etc., which 
moreover have considerable practical importance. It is still necessary to 
perfect methods capable of improving the comparisons and to research 
better secondary standards for routine use; the use of material standards 
in fact always carries a risk of deterioration which should be reduced to the 
strict minimum for primary standards. Finally, there is the application of 
new scientific discoveries leading to better definitions and units, and the 
BIPM should be in a position to bring them into play. 

The BIPM was thus led, apart from the verification of national stan- 
dards which today still constitutes its principal activity, to carrying out 
work of which certain parts have strongly marked the history of metrology 
[1]. 

The measurements of mass have given rise to various tasks: studies of 
the balance, methods of caHbrating sets of weights, determination of the 
values of British standards in metric units, effect of the subhniation of 



^ See appendix 6, p. 245, for the list of publications in which are listed the activities of the or- 
gans of the Metre Convention since 1875. 

^The international Metre and Kilogram were placed, with their verifications, in the lower 
vault of the Pavilion de Breteuil on September 28, 1889. The three keys needed to open the 
vault for the metric prototypes were given to the director of the BIPM. the president of the 
CIPM. and a representative of the National Archives in Paris. 



29 




Vault for the metric prototypes, above: the International Metre of 1889 in its metal case"; 
below; the International Kiloii;ram^. under its three glass domes, and its six check stan- 
dards. On the lower level are seen two thermometers, one of which is a maximum- 
minimum, and on the left a hair hygrometer. 




The International Metre and the International Kilogram of 1889 (life-size front view). 

30 

! 




platinum-iridium on the maintenance of mass standards, determination of 
the density of air, etc. The density of water, whence derive most volume 
measurements, was determined between 1895 and 1905 by three different 
methods; the result of this important work led to the acceptance for the 
mass of 1 cubic decimetre of pure water, with the air removed, at 4 °C 
under standard atmospheric pressure, the value 0.999 972 kg, that is 1.000 
028 dm^ for the volume of 1 kg of water, this result is still valid in 1975. 

Studies on measurement of length were not less numerous: determina- 
tion of the coefficient of expansion of the platinum-iridium alloy (compara- 
tor method and the Fizeau interferometric method), sharpening up some 
methods of cahbrating divided scales, measurement of geodetic base lines 
by means of invar wires and tapes, and cahbration of these, studies of stan- 
dards with flat and spherical ends, comparison of non-metric units (toise, 
yard, etc.) with the metre. 

We investigated materials less costly than platinum iridium suitable 
for making standards; the study of the expansion of nickel steels led to the 
discovery of some remarkable properties of several alloys, notably invar oi 
very low expansion, elinvar with a zero thermoelastic coefficient, platinite 
of expansion in the neighborhood of that of platinum and capable of being 
sealed to glass, nonmagnetic baros or nichrome, alloys of 42 or 58 percent 
nickel which have an expansion close to that of common glasses or of steel. 
All these alloys find application not only in metrology, but also in industry. 
Begun in 1896 on the initiative of J.-R. Benoit, these researches- are as- 
sociated with the name of Ch.-Ed. Guillaume, for whom they won the 1920 
Nobel Prize in physics. 

The interferometric measurements allowed establishing a link between 
the unit of length, embodied in the international Metre, and the length of 
light waves. Around 1890, A. A. Michelson (University of Chicago) 
proposed to substitute a wavelength for the platinum-iridium prototype; in- 
vited to come to the BIPM with his interferometer to apply his measure- 
ment methods, he thus established in 1892-1893, in collaboration with J.-R. 
Benoit, the ratio of the wavelength of the cadmium red line to the interna- 
tional Metre. In 1906, J.-R. Benoit, Ch. Fabry, and A. Perot made a similar 
determination with new procedures (Fabry-Perot etalons) confirming, with 
a better accuracy, the result given by Michelson 15 years earlier. The value 
of this wavelength, which served until 1961 for defining the Angstrom, was 
adopted in 1927 as a standard for spectroscopy and for interferometric 
measurements of length. 



" This difference of 28 parts per niillidii represents the approximation witii which the Kilogram 
of the Archives had been realized in 1799 with respect to its initial definition. This result, part 
of which must undoubtedly be attributed to luck, is remarkable if we consider the available 
means and the state of science at that epoch. The kilogram is found, in fact, to be represented 
by the mass of a cube of water which would have a thickness of not exactly 1 dm. but 
1.000 009 dm. only 0.9 fj.m greater! 



31 



Other work used applications of interferometry: study of graduated 
scales, measurement of industrial gages with flat and spherical ends, mea- 
surement of quartz (rock-crystal) etalons of 10 to 100 mm length for use as 
metric unit references, study of radiations used in metrology, determina- 
tion of the index of refraction of air, etc. 

In the field of thermometry, the work of J. Pernet and P. Chappuis on 
the gas thermometer led the CIPM to adopt the scale of the hydrogen ther- 
mometer as the "standard scale" of temperature in 1887, the first step 
toward the eventual adoption of the thermodynamic scale. Systematic stud- 
ies of the mercury thermometer by Ch.-Ed. Guillaume allowed making 
this instrument suitable for the measurement of temperature to a few 
thousandths of a degree in a well-defined scale. A consequence was that all 
the national metre prototypes distributed in 1889 were accompanied by two 
mercury thermometers of hard glass, with correction tables to convert their 
readings to the hydrogen-thermometer scale. 

In 1897-1898, J. A. Harker (Kew Observatory) and P. Chappuis carried 
out a comparison of the platinum resistance thermometer with the 
hydrogen thermometer; this was a prelude to the establishment of a practi- 
cal temperature scale which was adopted 30 years later. 

The acceleration of gravity, an important physical constant which is 
involved in the realization of several units (units of force, pressure, power; 
electric units, etc.), was determined at the Pavilion de Breteuil by 
Defforges in 1888, by the method of the reversible pendulum. The result 
obtained (referred to sea level at 45° latitude) led the 3d CGPM (1901) to 
adopt the conventional value 9.806 65 m/s- as the "standard value" of g-for 
use in the reduction to standard gravity of observations made at an arbitra- 
ry location. 

* 

This brief reminder shows how fertile was the activity of the BIPM 
during the first 50 years of its existence; although limited to the quantities 
mass and length, and to metrological studies related to the measurement of 
these quantities, this activity was essential to the development of scientific 
and industrial metrology. 

1925-1975 

Three salient facts characterize the second half-century of existence 
of the organs of the Metre Convention: 1st, the extension of the activities of 
the International Bureau of Weights and Measures to units and standards 
in the fields of electricity, photometry, and ionizing radiation; 2d, the 
greater and greater participation of the International Committee of 



32 



Weights and Measures in international cooperation in matters of scientific 
metrology, extending to standards of time and frequency; 3d, the revitaliza- 
tion of metrological methods, related to developments in several branches 
of physics (electronics, atomic physics, physics of solids, etc.) which have 
made possible for example, replacing the definition of the length and time 
units by definitions based on atomic properties. This evolution of the initial 
mission and fields of activity of the BIPM and CIPM is the natural con- 
sequence of the need for more and more precise measurement standards 
and of the necessity of assuring coordination of worldwide metrological 
work. 

Before presenting the activity of the BIPM during the period 1925-1975 
in the following chapters, it seems useful to outline the principal stages of 
this evolution. These stages have been marked by the creation of various 
Consultative Committees of the CIPM. 



Electricity and Photometry 

The idea of including electricity and photometry in the scope of the 
BIPM is very old. In deference to the conclusions voted by the "Interna- 
tional Conference on Electric Units" (Paris, 1884), a draft of an interna- 
tional convention was prepared by the French Government with an eye to 
entrusting the BIPM with the construction, verification, and maintenance 
of standards for electricity and light. This proposal, examined by the CIPM 
in 1885, was not followed up at the time even though most of the Member 
States of the Metre Convention had received it favorably. 

Later, the question of extending the activities of the BIPM to the elec- 
tric units was raised on different occasions.* It was nevertheless not until 
1921 that the BIPM received from the 6th CGPM the mission of "the 
establishment and maintenance of standards and references for electric 
units, and also the comparison of national standards or other precise stan- 
dards with these." In 1927, the CIPM decided to establish a Consultative 
Committee for Electricity (CCE), which held its first session in November 
1928. After the French Government had granted a small extension (285 m'-) 
of the BIPM grounds, new laboratories were constructed in 1929, adjoining 
the laboratories built in 1878, and the first comparisons of national stan- 
dards of electric resistance and of electromotive force were carried out at 
the BIPM in 1932. 

Unification of the methods of photometry and the question of the units 
of light also held the attention of the CIPM which in 1929 requested the 
CCE for advice on these subjects. The CCE then took the name 



" See a resume of this question in Proces-Verbaux C.I. P.M. 15. p. 169 (1933). 



33 



Consultative Committee for Electricity and Photometry, until 1933, at 
which date the CIPM decided to create a Consultative Committee for 
Photometry (CCP), distinct from the CCE. 

At its first session in June 1937. the CCP requested, in its report to the 
CIPM, the creation of a photometric laboratory at the BIPM for comparing 
national standards of intensity and of luminous flux. This laboratory was 
planned in the basement of the building constructed in 1929, and its essen- 
tial installations were finished in 1939. 

In 1971, the name of the CCP was changed to Consultative Committee 
for Photometry and Radiometry (CCPR); there is in fact more and more 
tendency to substitute energetic quantities (radiometry) for visual quanti- 
ties (photometry); this permits quantitative characterization of infrared and 
ultraviolet radiation as well as visible radiation. 



Thermometry 

In 1913, the 5th CGPM was concerned with the adoption of a ther- 
modynamic scale as a replacement for the standard hydrogen thermometer 
scale, and with the fixing of a certain number of thermometric reference 
points suitably chosen for establishing a practical temperature scale. To 
this end, a meeting of directors of national laboratories interested in the 
development of thermometric studies had been planned for November 
1914; events did not allow this meeting to take place; some 10 years later, 
the plan for a "Conference on Thermometry" was revived. In 1927, the 
CIPM was informed that the national laboratories of Germany, the United 
States of America, and Great Britain had agreed to adopt a common practi- 
cal temperature scale, as close as possible to the thermodynamic scale, 
based on fixed points and interpolation procedures. This scale was adopted 
provisionally by the 7th CGPM (1927) under the name "International Tem- 
perature Scale," then in a revised form, but still provisionally, by the 8th 
CGPM (1933). 

The convocation of the International Conference on Thermometry 
being repeatedly postponed, the USSR Institute of Metrology (1935) and 
the International Institute of Refrigeration (1937) proposed the creation 
under the CIPM of a Consultative Committee for Thermometry; the crea- 
tion of this committee was decided by the CIPM in June 1937.*^ 

The Consultative Committee for Thermometry (CCT) — for some time 
called the "Consultative Committee for Thermometry and Calorimetry" — 
met for the first time in July 1939, this meeting taking the place of that of 
the International Conference on Thermometry. Since its creation, the 



■' See the Proces-Verbaux C.I. P.M. 18. p. 96 (1937) for a chronological summary of the events 
leading to the creation of this Consultative Committee. 

34 



I 

I 



CCT has been concerned mainly with perfecting and extending the 
"International Practical Temperature Scale"; its work has also led to 
the adoption of the thermodynamic scale having a single fixed point, with 
the triple point of water as the fundamental fixed point and with the joule 
as the unit of heat replacing the calorie. 

Definition of the Metre 

The possibility of having a natural standard of length in place of a na- 
tional standard such as the International Metre has been a constant objec- 
tive of metrologists. The red line of natural cadmium, which had been 
proposed, could not, however, fill this role because it is not sufficiently 
monochromatic and would not permit defining the metre with a higher 
precision than that provided by the International Metre. 

Also, as soon as it was known how to separate the isotopes of certain 
elements and thus obtain practically monochromatic visible radiations, the 
possibility of using these radiations to define the unit of length came into 
view. The 9th CGPM (1948) consequently invited the large national labora- 
tories and the BIPM to pursue study of these radiations with the goal of 
possible establishment of a new definition of the metre based on the 
wavelength of a visible radiation. 

To study the advisability of such a change, the CIPM decided in Oc- 
tober 1952 on the creation of a Consultative Committee for the Definition of 
the Metre (CCDM). which held its first meeting in September 1953. Work 
carried out later in the national laboratories and at the BIPM on the 
metrological qualities of three proposed radiations led the CIPM to recom- 
mend, in 1958, the adoption of the wavelength of the orange line of krypton- 
86 as a new standard for the unit of length. On the 14th of October, 1960, 
the 11th CGPM unanimously adopted the change of the definition of the 
metre. 

Even though, after a reign of 70 years, the 1889 platinum-iridium Inter- 
national Metre preserved at the Pavilion de Breteuil has lost its position as 
the primary standard, the role of the BIPM has not diminished much; this 
role remains, to the contrary, essential for assuring uniformity of length 
measurements throughout the world. 

Its initial mission accomplished, the CCDM carried on its activities 
with three principal objectives: to perfect the 1960 definition of the metre, 
to recommend better secondary wavelength standards, and to improve the 
methods and apparatus for measurement of end-standards and line-stan- 
dards of length. 



35 



Time 



The units and standards of time and frequency were outside the 
responsibihty of the organs of the Metre Convention until 1954, the date at 
which the CIPM was led to consider these questions. At this time, the In- 
ternational Astronomical Union had just proposed a change in the defini- 
tion of the second and hoped that this definition would receive the interna- 
tional ratification of the CGPM. Under authorization from the CGPM, the 
CIPM in October 1956 approved the new astronomical definition of the 
second (the second of ephemeris time) based on the tropical year, a defini- 
tion which was ratified in October 1960 by the 11th CGPM. 

The appearance of "atomic" standards led the CIPM to create a 
Consultative Committee for the Definition of the Second (CCDS) in October 
1956 to study and propose a physical definition of the unit of time. Studies 
on the unit and scales of time had been, up to then, the province of as- 
tronomers; with the new techniques in the field of ultrahigh frequencies 
put into practice, these studies began to depend also on the competence of 
physicists. 

The CCDS held its first meeting in June 1957. Its work on atomic stan- 
dards of frequency and of time interval led to the 1964 provisional adoption 
of the frequency associated with a transition of the cesium-133 atom as the 
standard of time interval. In 1967, the 13th CGPM definitively adopted a 
new definition of the second, based on this same frequency, as a replace- 
ment for the astronomical definition. 

The CIPM and CGPM were subsequently requested to consider a time 
scale based on the second defined in 1967; an internationally adopted time 
scale is, in fact, indispensable for temporal synchronization of events in dif- 
ferent places. On the advice of the CCDS, the CIPM in October 1970 
adopted a definition of "International Atomic Time" (TAI) and, in October 
1971, the 14th CGPM authorized the CIPM to conclude necessary arrange- 
ments with the International Bureau of Time, the competent agency in the 
matter, for the realization of the TAI scale. Dissemination of the TAI with 
the aid of time signals thus permits putting at the disposal of users, not only 
the time scale, but also the SI unit, the second. 

Ionizing Radiation 

The metrology of ionizing radiation comprises measurements of x rays 
and y rays, radiations from radionuclides, and neutron measurements. Its 
importance has increased strongly since 1950. Nevertheless, the idea that 
the BIPM would play a role in this field is almost as old as the first steps 
toward a unification of radioactivity measurements, taken in the beginning 
of the century. It is interesting to trace the principal events which preceded 
the creation of the BIPM Section on ionizing radiation. 



36 



When Marie Curie constructed the first radium standard in 1911, she 
undoubtedly envisaged depositing it at the Pavilion de Breteuil. In fact, 
J. R. Benoit, then director of the BIPM, officially accepted this thin glass 
tube containing 21.99 mg of anhydrous radium chloride for safekeeping in 
1913; this constituted the international radium standard. This standard 
was replaced in 1939 by 1 of 20 standards fabricated by O. Hiinigschmid in 
1934; this new standard was removed from the BIPM in May 1940 for 
transfer into the country; it returned to the BIPM in 1959 and became its 
permanent property in 1961. 

In 1948, the USSR delegation to the 9th CGPM had already proposed 
that the BIPM organize comparisons of national radium standards with the 
international standards^" and that these latter be conserved at the BIPM. 
This proposal was again raised at the CIPM in 1952, and in 1956 the CIPM 
charged a commission with studying a possible extension of the activities 
of the BIPM to standards of radioactivity. After the report of this commis- 
sion, the CIPM created the Consultative Committee for Standards of Mea- 
surement of Ionizing Radiations (CCEMRI) in October 1958. 

At its first meeting in April 1959, the CCEMRI proposed: 

"that the scope of the BIPM be extended to the fields of radioactivity 
and ionizing radiations, and that it be the central agency: 

1st, for the definition of the quantities and units, 

2nd, for the establishment of international standards for measure- 
ment of activity and of ionizing radiations, neutrons included, taking 
into account the results of national, international, and other labora- 
tories and institutions." 

In October 1960, the 11th CGPM approved the action taken by the CIPM, 
and invited it to organize in the BIPM a Section on measurement standards 
for ionizing radiations, equipped with a laboratory and necessary scientific 
personnel. 

In its first three meetings (1959, 1960, and 1961), the CCEMRI defined 
for the BIPM a work program including in particular the organization of in- 
ternational comparisons. The new Section of the BIPM started operating 
in March 1961. 

After a new expansion (18 079 m-) of the grounds of the Pavilion de 
Breteuil, granted by the French Government, and after the 11th and 12th 
CGPM had voted three special contributions, two new buildings were con- 
structed for permanent laboratories of the Section for ionizing radiations; 
these laboratories were dedicated on September 29, 1964. Since 1969, the 
CCEMRI has comprised four sections (x and y rays, electrons; measure- 
ment of radionuclides; neutron measurements; standards of a-particle 
energy) which correspond to current activities of the BIPM Section for 
ionizing radiations. 

'"There still exists, in addition to the international standards preserved at the BIPM in 
Sevres, a replacement standard kept in Vienna (Austria). 



37 



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38 



Laboratories of the ionizing radiation section built in 1964 (l)uil(bnj; D of fig. 5). In tbe left rear, 
tbe 1929 laboratories. 

Other international organizations had already been concerned with the 
metrology of ionizing radiations ahead of the BIPM. In the first place must 
be mentioned the International Commission on Radiation Units and Mea- 
surements (ICRU), founded in 1925, which took a very active part in the 
creation of the new Section of the BIPM and in the preparation of its work 
program. It is necessary to also mention the laboratories of the Euratom 
Central Bureau of Nuclear Measurements and of the International Atomic 
Energy Agency, with which the BIPM maintains close relations. 

Units and the International System of Units 

The authority of the CGPM is recognized worldwide with respect to all 
matters concerning units and unit systems. Its decisions are taken over 
into the legislation of numerous countries, even if they do not yet adhere to 
the Metre Convention. 

In 1913, France had presented its draft of metric legislation to the 5th 
CGPM. The question of an international system of measurement units was 
not, however, truly submitted to the CGPM until 1948: the International 
Union of Physics requested the establishment of an international practical 
system of units; for its part, the French delegation proposed a draft of a 
universal system of measures as a basis for discussion. The 9th CGPM 
charged the CIPM "to open an official inquiry on the opinion in scientific, 
technical, and pedagogical circles of all countries, to centralize the respon- 
ses, and to issue recommendations respecting the establishment of a single 
system of practical measurement units, suitable for adoption in all the 
signatory countries of the Metre Convention." 



573-106 O - 75 - 4 



39 



The results of this inquiry led finally to the adoption by the 10th and 
11th CGPM (1954 and 1960) of the International System of Units, 
designated by the symbol SI in all languages. This coherent system, cur- 
rently based on seven base units (app. 4, p. 238) and two supplementary 
units, has been adopted by the principal international organizations; it is 
progressively replacing, in national legislation, the various systems (CGS, 
MTS, MKS, etc.) growing out of the metric system and the Anglo-Saxon 
measures in the countries where metric conversion is under way. 

For the study of questions about units, the CIPM had instituted a 
"Commission on a System of Units" in 1954; in October 1964, this became 
the Consultative Committee for Units (CCU). This Consultative Committee 
collaborates closely with the other international organizations'' which, in 
their respective fields, are led to concern themselves with units of physical 
quantities, and with their nomenclature and symbols. 

The CCU held its first meeting in April 1967. During its later meetings 
it prepared a document on the SI, supplemented with information on the 
practical realization of the definitions of the principal units [4]. 

At the moment, there exists no Consultative Committee for mass mea- 
surements, one of the basic activities of the BIPM, nor for gravimetry 
(absolute determination of the acceleration of gravity), another important 
activity of the BIPM. For the unit of mass, no natural standard has yet been 
proposed which can advantageously replace the International Kilogram, 
which has always accurately rendered the service expected of it; the CIPM 
has thus never had a motive for setting up a committee of experts on this 
subject. As to gravimetric measurements, discussions on this subject have 
taken place in the specialized committees of the International Union of 
Geodesy and Geophysics. 

* 

The creation of various Consultative Committees marks the evolution 
of the activities of the BIPM. It should not hide the permanent tasks which 
fall on the BIPM and which constitute the major part of its work: 

— international comparisons, most often organized by the com- 
petent Consultative Committees, which permit verification of the 
consistency of the basic determinations carried out in different 
laboratories; 

— verification of standards of numerous countries, verifications 
which since 1883 have given rise to the issuance of about 4000 cer- 
tificates, study notes, and reports; 



" International Electrotechnical Commission (lEC), International Commission on lllunima- 
tion (CIE). International Commission on Radiation Units and Measurements (ICRU). Interna- 
tional Organization for Standardization (ISO), International Union of Pure and Applied 
Physics (lUPAP), International Union of Pure and Applied Chemistry (lUPAC). 

40 



— the assistance that the BIPM supplies, within its means, to na- 
tional or international institutions in the field of source standards for 
metrology. 

Thus the BIPM has never ceased working effectively to assure the 
uniformity of measurements in the entire world, thanks to the propagation 
of the Metric System and then of its direct descendant, the International 
System of Units (app. 5, p. 243 ). 



'■^In the past, the BIPM had also been induced to lend its assistance in the preparation of na- 
tional laws on weights and measures; in 1933, it was proposed to the 8th CGPM to extend the 
scope of the organs of the Metre Convention to legal and commercial metrology, and to create 
a "Consultative Committee for Applied Metrology" under the CIPM. The independence of 
such an organism with regard to the CIPM and the BIPM having been judged preferable, this 
proposal finally resulted in the 1955 creation of the International Organization for Legal 
Metrology and of the International Bureau of Legal Metrology located in Paris. 



Bibliography 

[1] Documents diplomatiques de la Conference du Metre, Paris, Imprimerie Nationale. 151 
pages (1875). 

[2] La creation du Bureau International des Poids et Mesures et son oeuvre. Gauthier-Vil- 
lars, Paris, 321 pages (1927). See also, for example: 

Bigourdan, G., Le Systeme metrique des poids et mesures: son etablissement et 
sa propagation graduelle, avec I'histoire des operations qui ont servi a determiner 
le metre et le kilogramme. Gauthier-Villars, Paris, 458 pages (1901). 
Favre, A., Les origines du Systeme metrique. Presses Universitaires de France, Paris, 
242 pages (1931). 

Moreau, H., Le Systeme metrique: des anciennes mesures au Systeme International 
d'Unites. Chiron, Paris, in press. 

[3] Benoit, J.-R., Rapport sur la construction, les comparaisons et les autres operations 
ayant servi a determiner les equations des nouveaux prototypes metriques, Travaux et 
Memoires B.I.P.M. 7. 132 pages (1890). 

[4] Le Systeme International d'Unites (SI), 2d edition B.I.P.M., 40 pages (1973). The Inter- 
national System of Units (SI), 1974 edition, NBS Special PubUcation 330, 43 pages, 
and The International System of Units (SI), HMSO, London (1973). 



41 



CHAPTER II 



MASS 

In its Article 6, the Metre Convention charged the International Bu- 
reau of Weights and Measures with conserving the international prototypes 
of the metre and kilogram, and with comparing them with national stan- 
dards. 

The BIPM was thus the unique possessor of the starting-point stan- 
dards for all measurements of length and mass; it devoted itself entirely to 
these fields of activity and, naturally, to indispensable measurements of 
certain auxiliary quantities: temperature, pressure, density ... 

Later, the activities of the BIPM were extended to several other fields, 
for example to measurements of electric quantities, measurements in 
photometry and in the field of ionizing radiations, but none of these mea- 
surements was based on a new material primary standard; moreover, in 
1960, the change of the definition of the metre took away from the interna- 
tional prototype metre its role as primary standard for length measure- 
ments, so that the international prototype kilogram remains the only prima- 
ry standard conserved by the BIPM. 

Today, all sufficiently well equipped laboratories can, in principle, 
realize the units of length, time, temperature, and luminous intensity, 
which are defined in terms of natural properties of certain atoms or certain 
substances; on the other hand, these laboratories need the BIPM for the 
availability of the unit of mass and for realization of the units of electric 
current and amount of substance, whose definitions bear directly or in- 
directly on a rnass. It is the same for such derived units as those of force, 
pressure, and energy, which depend on the base units and particularly on 
the unit of mass. 

Conservation of the international prototype kilogram and verification 
of national mass standards thus continue to be a fundamental part of the 
mission assigned to the BIPM by the Metre Convention. 

The Prototype Kilograms and Periodic Verifications 

The International Kilogram 

In 1878, three platinum-iridium cyhnders (later identified by the sym- 
bols KI, KII, and Kill) were ordered from Johnson, Matthey and Co. of 



43 



London. They were polished and adjusted by A. Collot, in Paris, and com- 
pared with the Kilogram of the Archives by four observers in 1880 at the 
Observatory of Paris (the BIPM did not yet have available the scientific 
equipment needed for this work). 

Cylinder Kill, whose mass was found to be the closest to that of the 
Kilogram of the Archives, was sent to the BIPM, chosen as the interna- 
tional prototype kilogram in 1883, and ratified as such by the 1st CGPM 
(1889). The definition of the unit of mass resulting from this was explicitly 
stated by the 3d CGPM (1901) in the following terms: "The kilogram is the 
unit of mass; it is equal to the mass of the international prototype of the 
kilogram." This prototype, called "International Kilogram," is frequently 
designated by the symbol ^. 

The alloy of platinum (90%) and iridium (10%) had been chosen to 
make P as invariable as possible. On the one hand, this alloy is not subject 
to deterioration; on the other hand, the iridium gives it a hardness which 
reduces the wear on the prototype during the various manipulations to 
which it is subjected. The good quality of the polish which can be obtained 
also contributes to this invariability: it reduces the effect of high spots ex- 
posed to wear, and that of low spots which could retain dust. The density of 
the alloy (around 21.55 kg/dm'') is close to that of the platinum in the Kilo- 
gram of the Archives. Thus the volumes of these two standards being close- 
ly the same, the difference of the buoyancies produced by the air during 
their comparison was small, and the corresponding correction could be 
determined without too much difficulty. The surface of a mass standard 
should be as small as possible to further reduce the causes of variation 
either by wear or by adsorption of various substances. From this point of 
view, the most advantageous form is the sphere, but taking account of the 
difficulties of manufacture, adjustment, and especially handling, the 
minimum-area cyhndrical form is preferred, that is to say, a cylinder whose 
height is equal to its diameter' with, however, its edges rounded. 

Such a standard must naturally be handled with extreme care; we use 
specially adapted tweezers furnished with velvet or chamois skin, and kept 
sheltered from dust. This does not, however, dispense with using a small 
brush to wipe those regions which will come into contact with the standard, 
before using the tweezers. It is absolutely necessary to avoid dragging the 
standard on its support; this would inevitably cause a loss of mass. To 
make ^ lose a mass of 0.01 mg by uniformly wearing one of its bases, it 
would suffice to remove a thickness of metal of only 0.000 4 /xm, that is to 
say, to remove a little more than a layer of atoms. The surest means of as- 
suring the invariability of the unit of mass is therefore to make the least 
possible use of p. This is why it is removed only very rarely from the vault 



' The corresponding surface area is only 1.310 times that of a sphere of the same volume. The 
height of the International Kilogram, equal to its diameter, is about 39 mm; the area of each of 
its bases is about 12 cm- and its total surface area is 72 cm''^; its volume is 46.4018 cm^. 



44 



for the metric prototypes where it is kept, under three glass domes, well 
sheltered from pollution (p. 30). 



Other Prototype Kilograms 

In 1882, 40 platinum-iridium cylinders were ordered from Johnson, 
Matthey and Co. They were delivered in 1884 and their density was deter- 
mined; they were then polished and adjusted (to about ± 1 mg) by A. Collot 
at the BIPM. The numbers 1 to 40 were assigned to them.- Counting the 
standards KI and KII which remained available after the choice of the In- 
ternational Kilogram, 42 Prototype Kilograms^ were thus available, in all 
respects similar to p. These standards, after cleaning with steam and al- 
cohol vapor, were compared among themselves in a very large number of 
combinations of pairs, and each was compared directly with ^. 

During the 1st CGPM, 34 standards were assigned by lot to those 
Member States of the Metre Convention which had requested them. Proto- 
type Nos. 9 and 31 were assigned to the BIPM as working prototypes; KI 
and No. 1 became the two check standards for p and were deposited in the 
same vault; Nos. 7, 8, 29, and 32 remained available. 

Subsequently, to be able to respond to requests, 23 other prototype 
kilograms were constructed from 1929 to 1974, starting with cylinders 
prepared either by Johnson, Matthey and Co. or by Comptoir Lyon-Ale- 
mand at Paris, some of them recast from old prototypes. Nine of them were 
adjusted at the BIPM. These 23 prototypes carry the numbers 41 to 63. 
Only the last remains available, the 22 others having been assigned, along 
with No. 29. 

In 1905, prototypes No. 8 and No. 32 became two new check standards 
for p. In 1925, No. 7 replaced check standard No. 1 which had been sub- 
ject to an accident during a weighing.^ In 1938, prototypes 43 and 47 were 
used to increase the number of check standards for p, which brought this 
number to six. 

Finally, No. 25, assigned to France and which had been given to the 
Paris Observatory, was ceded to the BIPM in 1958 and has become a proto- 
type for infrequent use. 



These numbers are marked on the sides of the cylinders by a slight depolishing through a 
stencil. 

■■"Mass standards of 1-kg nominal value are called "Kilograms." The designation "Prototype 
Kilogram" (or simply "prototype") is generally reserved for platinum-iridium Kilograms. 

It was then noticed that prototype No. 1 had a slightly convex base; this construction defect 
was the cause of its fall. 



45 



Figure 1. Housing used for the protection of prototype Kilograms and for transporting them 
inside the laboratory. The prototype Kilogram K rests on a quartz plate Q. which in turn 
rests on a brass cylinder P' attached to the plate P. Its possible lateral displacements are 
limited by a brass crown L provided with a silver ring A whose inside diameter is 3 mm 
greater than the diameter (39 mm) of the Kilogram. The latter is covered by two glass domes 
C and C, one of which is held in place by blocks resting on the rim at the base of the dome. 
The two blocks E are fixed: block F. detachable, can be immobilized by the key S to assure 
closure of the housing. 

The housing for the International Kilogram is itself protected by a third dome resting 
on a ground-glass plate. 

46 



Periodic Verifications 



Article 6 of the Metre Convention provided for periodic comparisons 
of national prototypes with the international prototype or its check stan- 
dards; it is the duty of the BIPM to organize these. 

The first periodic verification of the Prototype Kilograms was carried 
out between 1899 and 1911. It involved 18 national prototypes, 4 prototypes 
not yet assigned, the 2 working prototypes of the BIPM, 2 other BIPM 
prototypes designated C and S whose forms were respectively a cylinder 
and a truncated sphere, and finally prototype No. 1, check standard for p. 

This important comparison was carried out without preHminary clean- 
ing of the prototypes. The results, communicated to the 5th CGPM in 1913 
[1], made it evident that the masses of most of the prototypes had practi- 
cally not changed relative to their values in 1889. In particular, the masses 
of those which had not been used were often found constant to a few micro- 
grams. This was the case for No. 1, check standard for ^, for Nos. 8 and 
32, new check standards since 1905, and also for No. 21, assigned to Mex- 
ico and which had made the round trip without being unpacked. On the 
other hand, the masses of certain prototypes which carried visible signs of 
wear or accident had diminished appreciably. One of the BIPM working 
prototypes (No. 31). which had been handled with great care but had been 
subjected to particularly intensive use, had itself lost 21 /xg. The possibility 
of regularly comparing the working prototypes to one or two check stan- 
dards and the recent increase in the number of check standards indicated 
that conservation of the unit of mass was assured to better than 0.01 mg for 
many years, even having recourse to p only very rarely. 

In light of this reassuring conclusion, the CIPM waited nearly 30 years 
before requesting the BIPM to organize the second periodic verification of 
National Prototype Kilograms, preceded this time by a comparison of p 
with its check standards. This comparison was carried out in June 1939 
[2]; it involved the four old check standards (KI, Nos. 7,8, and 32) and the 
two new ones, Nos. 43 and 47, to which it was necessary to assign values. 
This comparison was itself preceded by comparisons among check stan- 
dard No. 8, several prototypes not yet assigned, and the BIPM prototypes 
C, S, No. 9, and No. 31. All these kilograms were cleaned before weighing 
with a chamois skin impregnated with alcohol and then with redistilled 
benzene. The results obtained were not very satisfying: they seemed to 
show for the four old check standards and the working prototype No. 9 an 
increase in mass (of 0.03 to 0.08 mg) relative to their values in 1889; work- 
ing prototype No. 31. whose bases carried numerous lines and traces of 
rubbing seemed to have conserved its original value. The following ex- 
planation was put forth: although ^ is kept under three glass domes, of 
which the largest, furnished with a stopcock by which a partial vacuum was 
made, rested on a ground-glass plate, the other prototypes are only placed 
on their support under two domes which rest on a metal plate (fig. 1). 



47 



Changes of the air around them have probably been more important than 
around ^ and it has been possible for the formation on these check stan- 
dards of adherent deposits which a washing in steam or alcohol vapor, not 
done in 1939, would doubtless remove. 

The following years were put to profit in studying the cleaning of 
prototypes. The efficacy of washing with steam was recognized and it was 
decided to apply this treatment, before each important group of com- 
parisons, to prototypes previously cleaned with pure benzene and pure 
alcohol. Before each weighing, a fine hair brush was also used on the en- 
tire surface of the prototype to remove most of the dust. 

In 1946, a new comparison was made among its six check stan- 
dards (KI, Nos. 7, 8, 32, 43. 47), and the working prototypes Nos. 9 and 31. 
For the four old check standards, the small changes (— 0.03 to + 0.04 mg) 
found relative to the 1889 values showed the importance of cleaning and 
washing the prototypes as regards the confidence which can be placed in 
the weighing results [3]. This comparison was followed, between 1948 and 
1953, by the second periodic verification of the national prototype kilo- 
grams. Thirty-three prototypes participated therein. The results, presented 
to the 10th CGPM in 1954 [4], demonstrated the perfect stabiHty of certain 
prototypes; in many cases, the verified variation of others could be ex- 
plained. 

No other verification of national prototype kilograms has been or- 
ganized since. 

Thus, as is desirable, ^ has been used only in rare circumstances: 
comparisons before 1889 (when it was involved in some 40 weighings), com- 
parisons of 1939 (7 weighings), and of 1946 (14 weighings). 

Determination of the Mass of Kilograms 
Outside the Periodic Verifications 

The BIPM can naturally study each kilogram for which a request is 
made. Thus since 1953, date of the end of the second periodic verification, 
it has determined the density and the mass of 7 newly constructed proto- 
types and it has verified 16 other prototypes which are, for the most part, 
national prototype kilograms. 

For these comparisons, the BIPM has available its two working proto- 
types, Nos. 9 and 31. Since these are subject to intensive use (each is 
manipulated from 300 to 500 times per year) and their surface is con- 
sequently exposed to certain pollution and to possible wear, it is necessary 
to redetermine their mass from time to time. To avoid the need of removing 
one or two check standards for P from the vault, an operation which 
requires CIPM authorization, the CIPM decided in 1956 to place at the 
disposal of the BIPM a prototype for infrequent use. No. 25, which should 



48 



be used only rarely. It is kept in a vault to which the Director of the BIPM 
has easy access. 

The masses of prototypes Nos. 9, 31, and 25 had been determined at 
the time of the second periodic verification, then in 1957 by comparison 
with the six check standards for ^, and in 1965 by comparison with two 
check standards Nos. 8 and 43. Since that date, the masses of Nos. 9 and 31 
have been redetermined by comparison with No. 25, on two occasions, in 
1968 and in 1973. A redetermination is anticipated about every 5 years. 
The study of the history of the mass of these two prototypes is very in- 
structive (fig. 2). It shows that the loss of mass by wear can be extremely 
small for prototypes that are manipulated with great care, but that on the 
other hand their exposure to the laboratory air produces a pollution of their 
surface which betrays itself by a gain in mass of the order of 3 fig per year. 
Cleaning with a solvent followed by washing in steam from twice distilled 
water makes them recover their initial mass very closely. 



1 kg+300jjg-- 



+ 200 -- 



+100 -- 



+ 0 



oo 



N°9 



N°31 




4- 




1875 



1900 



4- 



4- 



1925 



1950 




0,1 mg 



1975 



Figure 2. History of the mass of the BIPM working prototypes Nos. 9 and 31. For the two 
prototypes, we clearly see the effect of steam washing L practiced in 1946 and 1965. as well 
as the increase of their mass between washings and since 1965. This increase is less for No. 
9 than for No. 31 whose surface is rather strongly grooved. The values obtained from 1903 
to 1933 result from a smaller number of weighings and are traceable to ^only in a very in- 
direct way; they are less reliable than those of 1889 and 1939. Between these two dates, the 
wear on No. 31, used very intensively, was compensated by the mass gain due to pollution 
of its surface. The discontinuities A correspond to accidents undergone by the two proto- 
types in September 1949 and February 1951, respectively. 



49 



Thanks to research pursued since the beginning of the century on the 
fabrication of mass standards in a material less costly than platinum-iridi- 
um, there are now available alloys whose stability is quite satisfactory. In 
particular, stainless steel containing about 20 percent nickel and 20 per- 
cent chromium has been used for the construction of some 15 national kilo- 
grams which have been studied by the BIPM. The density of this alloy 
being around 7.8 kg/dm^, the volume^ of these kilograms is about 82 cm^ 
greater than that of the platinum-iridium prototypes. As a result, when the 
mass of a stainless steel kilogram is determined by comparison with a 
platinum-iridium prototype, the different values of air buoyancy on the two 
standards requires the application of a correction whose value reaches 
nearly 100 mg at the BIPM. This correction can not, at this time, be calcu- 
lated to better than 0.05 mg, by reason of the limited precision with which 
the density of air is known as a function of ambient conditions (pressure, 
temperature, humidity). 

But it must be noted that if a laboratory, starting with a stainless steel 
standard kilogram, calibrates secondary standards of the same material, no 
uncertainty due to air buoyancy affects this measurement; on the other 
hand, if a platinum-iridium prototype kilogram is used, the uncertainty in 
the correction for air buoyancy at that moment enters into the determina- 
tion. 



Balances and Methods Used for Comparisons 
of Kilograms; Auxiliary Measurements 

Balances and Weights 

The only method allowing comparison of two masses with a precision 
better than 1 X 10 that is, with an uncertainty less than 0.01 mg for 1-kg 
masses, consists of comparing their iveights by means of a balance. Since 
its beginning, the BIPM has been equipped with several "equal-arm" 
balances. It is easily realized that it is not possible to adjust the lengths of 
the arms of a balance beam with the desired precision, that is, to better 
than 2 nm for arms of 0.2 m. One is thus led to use the balances in a double- 
weighing operalion, either by Borda's method which consists of substitut- 
ing one mass for the other on the same platform, or by Gauss's method in 
which the masses on the two platforms are interchanged. The Bunge 
balance and the Rueprecht balance, which until recently were the two prin- 
cipal balances used at the BIPM for Kilogram comparisons [5], were 
designed for operation with Gauss's double weighing. The observer 
manipulates the balance from a distance of 4 m, the balance case remain- 



■''The stainless steel Kilograms have a volume of about 128 cm^. They have the form of a 
cylinder with rounded edges, whose height, equal to the diameter, is about 55 mm. 



50 



ing closed; in particular, he controls the movement of the transposition 
mechanism which accompHshes the permutation of the masses. Tempera- 
ture variations which would be caused by the approach of the observer are 
thus avoided. 

The masses of the Kilograms to be compared are generally very close; 
if such is not the case, additional loads of known value are added to the 
standard of lesser mass, in preparing for the weighing. For each of the two 
placements of the masses mi and m-z on the platforms, the beam inclination 
corresponding to its equilibrium position is determined. If the lengths of 
the two arms of the beam are designated by /i and I2, these very small 
inclinations are proportional to m,/, — m-zk for the first arrangement and 
m A\ — m^l-z for the second. Their difference a is proportional to 

— m-2li) — (m-j/, — mil>) = (m, — m>) Hi + I-,) 

The coefficient of proportionality is related to the sensitivity of the balance 
which is sHghtly variable in high-precision balances by virtue of the close 
proximity of the beam axis (edge of the central knife) and its center of 
gravity. This coefficient is determined for each weighing by means of small 
masses m'l and m'> (for example, 100.5 mg and 100.0 mg) whose difference 
is well known and which are placed, by means of a remote control 
mechanism, on parts called stirrups which form part of the platform 
suspension; the platforms remain loaded by the Kilograms under com- 
parison. The additional inclination (3 which results is proportional to 

from this is easily derived 

mi-m2 = ~(m i — m ■,)■ 

The availability, in the balance case, of two identical sets of additional 
loads allows loading the beam on either the left or the right. 

In practice, a graduated scale is observed through a telescope by 
reflection in a plane mirror attached to the balance beam. When the latter 
oscillates, the graduated scale appears to march past a fixed reference 
point. The maximum excursions successively attained to the right and left 
are noted. Starting with three successive excursions Xi, xo, X3, the calcula- 
tion of the excursion x corresponding to the equilibrium position of the 
beam can be made: x — {xx + 2x-i + x-a) 1^. Five successive excursions are 
generally noted, allowing judgment of the regularity of the oscillation. 
Similarly, one is not content with a single transposition of the masses but 
usually uses 10 of them; this allows determining 6 equilibrium inclinations 
for one disposition of the masses and 5 for the other. The agreement of suc- 
cessive equilibrium positions indicates the quality of the weighing and the 
good condition of the balance. 

To avoid having the transposition mechanism come into direct contact 
with the Kilogram base during a weighing, the kilograms in fact sit on 



51 



platinum auxiliary platforms. The masses of the auxiHary platforms are ad- 
justed as well as possible; their difference, which can reach 0.02 mg, is 
eliminated from the results of the comparison by a complete weighing com- 
prising two parts between which the Kilograms are interchanged without 
interchange of the auxiliary platforms. 

The Bunge balance, in service since 1879, has shown itself difficult to 
regulate in a lasting way. After the fall of the two BIPM working prototypes 
(No. 9, in 1949, during the preparation for a weighing, and No. 31, in 1951, 
in the course of a weighing) in this balance, we have stopped using it. 

The Rueprecht balance, delivered to the BIPM in 1878, was complete- 
ly overhauled and modified by its maker in Vienna in 1900-1902 [71. In 
1937, after prolonged and intensive use, it was sent to C. Longue, in Paris, 
who succeeded in restoring it to practically its original quality. Since then, 
we have applied ourselves mostly to improving its installation, notably its 
thermal protection and the precision of measurement of temperature inside 
the balance case. Despite the care with which this balance has been used, 
it has probably lost part of the exceptional quality that it previously had. In 
fact, from its last reconditioning until the end of 1974, it has been used for 
about 1000 complete weighings, representing about 250 000 oscillations of 
the beam. The releasing oi the balance, which places the knives in contact 
with their flats, has thus been repeated about 30 000 times. The frequency 
of use now tends to diminish since the BIPM has had available since 1970, 
a new balance placed into service in 1973, based on an entirely different 
concept and having higher precision (see p. 56). 

Calibration of Multiples and Sub-Multiples of the Kilogram 

The accuracy of a weighing depends primarily on the accuracy with 
which are known the smallest masses, notably those which are used as ad- 
ditional loads in Kilogram comparisons. Calibration of a series of masses 
allowing passage from the Kilogram to the milligram is thus a fundamental 
operation. 

Consider a series comprising the masses m^oo, "1200, ^'200, and mioo of 
nominal values 500 g, 200 g, 200 g, and 100 g, and also masses mso, m-^o, 
m'20, and mu) whose sum of values, designated by Xioo, is nominally equal 
to 100 g. The methods used for calibrating such a series always come back 
to a determination of the small difference e which exists between combina- 
tions of different masses giving the same nominal value. Thus, commenc- 
ing by comparing a Kilogram with the set of masses of nominal values 100 
g to 500 g, we obtain: 

mm)+ m2W)+ m'2m)+ mnM= 1 kg+ Ci 



52 



and then, for example, the following comparisons are made: 







m ' ^ ,1 — t — TYi . . \ — 
200 1 ffl\{)0} — 


62 


'''■dOO 


\''t200 r 


"i 20(1 I iloo; — 


63 


'"'20() ' 


^ 1 00 ~\~ 


2011 1 ZiKIII ) — 








(m'2oo+ mim,) = 




^200 




Ttl 200 — 




^200 




('Wioo + Sioo) = 


€7 


^200 




(^100 + 2ioo) = 


68 


^100 — 




2 100 — 


€■1 



This linear system of nine equations in five unknowns [m-Mn, ^200, m'ooo, 
^100, Xioo) is reduced by the method of least squares to a linear system of 
five equations in five unknowns which can be solved by hand, but for which 
a computer is now preferred. 

The next step follows analogously since 2ioo= ^50+ ^20+ ^'20+ 
is now known. For the final step, the series must be complemented by a 
supplementary 1-mg mass. The final result is the calibration of masses of 
the order of a milligram with an uncertainty of about 0.5 ^lg. 

Naturally, the same method is appHcable in going from 1 kg to 10 kg. 
The BIPM has available balances adapted to various loads which occur in 
these different weighings. 

Hydrostatic Weighings and Correction for Air Buoyancy 

Accurate weighings require the application of a correction for "air 
buoyancy." Its calculation involves the volumes of the standards being 
compared, volumes which are generally determined by hydrostatic 
weighings. 

A hydrostatic weighing consists essentially in determining the mass of 
liquid displaced by a submerged body. If the volume of the body is known, 
the density of the liquid can be deduced; conversely, if the liquid density is 
known, the volume of the body is obtained. The volume of a Kilogram is 
thus determined by using water as the immersion liquid. 

A hydrostatic weighing is carried out by the Borda double weighing 
procedure. In a first operation, the submerged body is suspended from the 
balance and equilibrium estabHshed: in the second operation, the body is 
freed from the suspension system by means of a mechanism inside the im- 
mersion vessel, and equilibrium is reestablished by substituting masses on 
the platform of the same side. This yields equality between the apparent 
mass m — of the submerged body (its real mass reduced by the mass of 
the displaced liquid) and that of the mass added to the platform (real mass 
reduced by the mass of the displaced air). 

By weighing the same body in air, its apparent mass m — (real 
mass reduced by the mass of displaced air) is, in fact, determined. 

Introducing the volume V of the body under study, and the densities 



53 



Pw and Pa of the liquid and of air, it is seen that one has determined the two 
quantities m — Vp.^ and m — Vp^^. whose difference is V{pw — Pa)- 

For water, we calculate p^ for the conditions of measurement starting 
with the value 999.972 kg/m'' [6,7,8] assumed for standard reference con- 
ditions (4 °C (maximum density), standard atmospheric pressure, absence 
of dissolved gas), and using the expansion table of Chappuis [9]. For air, 
we calculate Pa starting from ambient conditions: temperature and relative 
humidity in the balance case, and atmospheric pressure, by means of for- 
mulas due to Broch [10]. 

One must allow for the fact that the acceleration of gravity does not 
have exactly the same value at the level of the submerged body and at the 
level of the masses on the platform. 

The volumes of Kilograms are thus determined to about 1 X 10"\ They 
enter into the comparisons through calculation of the correction due to air 
buoyancy. 

The hydrostatic balance which was dehvered to the BIPM in 1891 to 
replace the balance then in service has itself been replaced in 1963 by a 
new balance of more recent concept. 

Recent Balances and Current Studies 

New Hydrostatic Balance; Density of Water 

This balance (fig. 3), whose assembly was accomplished in 1964, is 
furnished with a remotely operable mechanical device for substitution of a 
mass on one level of the platform, for a mass on the other level of the same 
platform. 

The small additional loads used in determining the balance sensitivity, 
that is, actually, for calibrating the divisions of the reading scale "in mass," 
can be placed on the stirrups or removed without the observer coming near 
the balance. We have concentrated on checking and improving the 
uniformity of the water temperature in the immersion vessel. With this new 
instrument, the density of Kilograms can be determined with a reproduci- 
bility better than 1 X 10^^. Figure 4 gives the principle of such a measure- 
ment. 

This balance was reconditioned in 1973-1974. On that occasion, it was 
equipped with a brake which permitted limiting the amplitude of oscillation 
to a determined value, and with a mechanism for changing masses on the 
two levels of the right-hand platform, identical to that which already ex- 
isted for the left platform. It will be possible to carry out differential hydro- 
static weighings between two baths (for example, water at different tem- 
peratures or of different isotopic constitution) with the help of two sub- 
merged bodies of approximately the same mass and volume. 



54 




Figure 3. The hydrostatic balance installed in 1963. C. upper case containing the balance: C ', 
lower case containing the immersion vessel V; F, beam; P, two-level platform; E, observa- 
tion scale: L, projector: O, position of the observer operating the balance controls, from a 
distance of 2 rn. The thermal shields have been removed. 



The precision of this balance has allowed us to undertake, starting in 
1967, the study of the variation of density of water as a function of its 
isotopic constitution [11 1, that is to say, of its content of heavy isotopes 
'^O, '^O, and -H. The body used for the hydrostatic weighings is a stainless 
steel cylinder of approximately 1 kg mass, whose volume and expansion 
coefficient have previously been determined. Observations have been 
made on seven samples of water which have been distilled twice before the 
weighings: two samples from Greenland (one in the solid state at an al- 
titude of 2900 m, the other from a small lake near Thule), three samples of 
sea water (two from the Atlantic and one from the Mediterranean), and two 
samples of water artificially enriched in ^^O. At the end of each weighing, 
a sample was taken for analysis at the Saclay Center for Nuclear Studies. 
The values obtained cover a range of 0.02 kg/m^, which represents the 
maximum spread due to only the difference of isotopic composition which 
can be encountered in practice between the densities of any two samples 
of natural water. A formula established from these results allows calcula- 
tion of the difference of densities between any two natural waters of known 
isotopic constitution to about 0.001 kg/m'l 

This study poses anew the problem of the density of water: it demon- 
strates the need for determining in an absolute way, at a reference tem- 



573-106 O - 75 - 5 



55 



perature, the density of water of known isotopic constitution and for malc- 
ing new measurements of the variation of water density as a function of 
temperature. Several laboratories have already started these studies at the 
request of international organizations cooperating with the BIPM. 

Single-Platform Balance for Comparing Kilograms 

For some decades, several national laboratories have studied balances 
having an essential improvement which consists in realizing the in- 
terchange or substitution of the masses being compared while maintaining 
contact between the knives and the flats. This largely avoids disturbing the 
molecular relations which become established when the knives are in con- 
tact with the flats; there results a better constancy of the length of the 
beam arms and consequently a better accuracy of the balance. 




t 



Figure 4. Scheme of utilization of the hydrostatic balance, a) First operation. The submerged 
body K (Kilogram) of mass m is suspended from one of the platforms. The balance is 
equilibrated with the mass on the same side and t (tare) on the other platform, b) Second 
operation. The body K is separated from the suspension device. The balance is again 
equilibrated, this time with the mass m2, the tare t being unchanged. 

The mass m2 — nii has thus been substituted for the apparent mass m — m^. where m„ is 
the mass of the displaced liquid. A correction must be applied to take account of the air 
buoyancy on the masses on the left platform, on the (jne hand, and on the other hand, of the 
variation in the acceleration of gravity corresponding to the vertical distance between K and 
this platform. The masses of the auxiliary platforms Pi and P2 are eliminated from the 
results thanks to a second weighing in which the masses mi and m-z are associated with P2 
and Pi respectively. 



56 



The balance developed by the NPL is a classical two-platform balance 
with three knives; the knives remain in contact with the flats, but under 
reduced load, during interchange of the masses. 

The one studied at the NRLM also has three knives and two platforms, 
but the latter have two levels. Substitution of the masses is effected on the 
two levels of the same platform while the knives remain in contact with 
their flats and under constant load, even without the balance oscillations 
being interrupted. 

The balance studied at the NBS is, on the contrary, a balance having 
a single platform and two knives (the second platform is replaced by a 
counterweight); the knives and flats remain in contact and under constant 
load during substitution of the masses. The second prototype brought out 
by the NBS, called balance NBS-2 [12], was put at the disposition of the 
BIPM in 1970 (fig. 5); its permanent installation in an isolating booth was 
finished in 1972 and verification weighings were soon started. The balance 
is necessarily operated from a distance. Determinations of prototype Kilo- 
grams with this balance began in 1973 after a first improvement of its ther- 
mal stability. 

The constant load on the knives during the substitution of masses is 
such as to strictly maintain the contact conditions and to give the balance 
a remarkable accuracy. Replacing the second platform by a counterweight 
reduces the number of knives to two, which simplifies adjusting their paral- 
lelism; on the other hand, this practically limits the use of the balance to 
the comparison of kilograms; furthermore, two interchangeable counter- 
weights must be available, one of platinum-iridium and the other of stain- 
less steel, used accordingly in the comparison of prototype Kilograms or of 
stainless steel Kilograms. To compare a stainless steel Kilogram with a 
prototype Kilogram, the platinum-iridium counterweight is used. 

Figure 6 shows the releasing of the balance, that is, the passage from 
the rest position (knives and flats separated) to the weighing position; 
figure 7 indicates schematically the functioning of the mechanism which 
permits mass substitution with constant loading. 

The balance is equipped with a carrier capable of holding six Kilo- 
grams and allowing the placement of the selected mass on the platform. It 
is then possible to compare six standards (or fewer) in all their combina- 
tions, two-by-two. As an example, such a comparison of four Kilograms 
lasts about two and one-half hours. Each comparison of two Kilograms is 
carried out in terms of the counterweight. One determines, according to 
the maximum excursions read on a scale, the equilibrium positions of the 
beam under the following different loads: a) Kilogram A, b) Kilogram B, c) 
Kilogram B + added weight, d) Kilogram A + added weight, e) Kilogram A. 
The added weight is a small rider of known mass which serves to calibrate, 
in terms of mass, the value of one division on the scale. These observations 
being more numerous than needed for determining the difference between 
the masses of Kilograms A and B, the statistical uncertainty of this dif- 



57 




Fipui e 5. The NBS-2 siiifjle-platforni Ijalance of the BIPM. C. Cdunterweight attached to the 
beam F: X. assembly of crossed plane knives: A. stops for arrestment and alinement: S, 
Cardan suspension for platform P: T. circular carrier capable of holding six Kilograms K 
(here, of platinuin-iridium) and of placing one of them on P: Q. air-tight passages for the 
nifchanical ccmtrols and measuring circuits (temperature, pressure, humidity). The upper 
part E (it the air-tight encl(jsure has been raised and part of the thermal protection removed. 



58 




® 





Figure 6. Releasing in balance NBS-2. (a) Rest position. The beam F. to which is fixed the 
counterweight C, rests on the movable stop M in its high position, and on the two alinement 
stops located on both sides of the beam. The platform rests on alinement stops A' through 
its stirrup E. (b) Intermediate position. During the first phase of lowering stop M. the prin- 
cipal knife conies into ccmtaci with its plane, the beam pivots slightly and no longer rests on 
stops A. (c) Weighing position. During the second phase of lowering stop M. the end knife 
comes into contact with its plane fixed on the stirrup E of the platform and raises the stirrup 
which no longer rests on slops A'. The balance can oscillate freely. 

Reverse operation of the movable stop M allows passing from the weighing position to the 
intermediate position and then to the rest position. 



59 





@ ® © 

Figure 7. Balance NBS-2; scheme for suhstitutin<i masses witli constant loading, la) 
Weighing position. The mass K (Kilogram) rests on the platform P. (h) The carrier T is 
raised and comes into contact with K. (c) The carrier achieves its lifting motion; the beam 
tilts slightly until the small sphere S comes into contact with the stop B attached to the 
balance frame. Carrier T then raises K which is no longer in contact with platform P. The 
loads on the knives thus remain practically constant. 

The carrier can then displace K perpendicularly to the plane of the figure and bring 
another mass in above the platform. In lowering, it places this mass on the platform (posi- 
tion shown in (b)). then returns to the weighing position (a). 

ference can be deduced. Various improvements which have been made, 
especially that giving operation of the balance under an air-tight dome, 
have allowed reducing the standard deviation^ of such a comparison to 
2Atg. 

It is thus possible to determine the mass of a prototype Kilogram with 
a standard deviation of the order of 1 /xg, making only a small number of 
measurements, under the condition, however, that the masses of the BIPM 
working prototypes are known with sufficient accuracy. Since this is not so, 
we foresee a new determination in the near future, relative to p, of its six 
check standards and the working prototypes, followed by the third periodic 
verification of the prototype Kilograms. 

Problems Posed by Improvement of Weighing Precision 

We have already seen that the correction for air buoyancy limits the 
comparison of a stainless steel Kilogram with a prototype Kilogram. 

ForiTiulas used in various laboratories can give corrections for this 
which differ by 20 /xg. That becomes entirely disproportionate relative to 

•'There are 68 chances in 100 that the random error, in absolute value, is less than 1 standard 
deviation, and 99.7 chances in 100 that it is less than 3 standard deviations. 



60 



the reproducibility which can currently be achieved in weighing. It is there- 
fore appropriate to restudy the estabHshment of formulas giving the density 
of air as a function not only of pressure, temperature, and relative humidi- 
ty, but also as a function of its composition, and to study simple and rapid 
methods for determining this composition. Another method would consist 
in experimentally determining the air density in the balance case itself or 
in an enclosure communicating with it. The air-tight case of balance NBS-2 
would be well adapted to the latter solution. 

We have seen also that, even with the earlier balances, one could mea- 
sure the increase of mass of a prototype, due to pollution of its surface, over 
a period of 5 years. We can now measure it over a period of 1 year. In the 
past, it was shown that it is necessary, before each important series of com- 
parisons, to submit the prototypes to a cleaning followed by washing in 
steam, but one was not certain of the stability of prototypes after this treat- 
ment. Whereas the systematic measurements made towards 1965 per- 
mitted no conclusion, those which were carried out in 1974 have clearly 
shown that the masses are stable and that the weighings can be carried out 
without delay (fig. 8). 

It is equally known that the importance of wear and pollution of the 
prototypes is related to their surface condition. It is therefore fitting to im- 
prove the polish. The BIPM has used a paste with a diamond-powder base 
to achieve poHshes of excellent quality which could lead to an appreciable 
improvement in the stability of prototypes. 

Thus, despite the imperfections inherent in a material standard, but 
thanks to precautions taken for its conservation, the International Kilo- 
gram has without fail played its role as a basic standard for nearly a centu- 
ry, through the intermediary of its check standards and some of their proto- 
types. 

It would be very satisfying to define the unit of mass as a multiple of 
the mass of an elementary particle or of an atom, which would constitute an 
absolute guarantee of stability. Now, although the ratios of various atomic 
masses can sometimes be determined with an uncertainty less than 1 X 
10"'', the unit of atomic mass (1/12 the mass of the atom of carbon 12) is 
currently known to only about 3 X 10"". Despite the constant progress real- 
ized in this field, there is httle hkelihood that in the near future one can 
gain the factor 1000 which would allow considering the adoption of an 
"atomic" definition of the Kilogram. 



61 









o 


standard deviation 

o 












O O 




o 





10 February 20 February 1 March 1974 8 March 

Fij:ure 8. Hislory of the mass of three prototype Kilograms after a cleaninji-washiiig, and stan- 
dard deviation of each comparison. With tlie scheme used for the determination of the mass 
of each prototype, the standard deviation crof the value (jf this mass is equal to 0.7 times the 
mean standard deviation of comparison (2 jUg). say 1.4 /Ag. The error bars correspond to ± 
3(T. say about ±4/jg. 

The figure shows that after a cleaning (benzene and pure alcohol) followed by washing 
(jet of steam from twice-distilled water), prototypes N<is. 46 and 52 have not changed signifi- 
cantly during the duration of this study. On the other hand. No. 39 shows an instability 
proliably due to its bad surface condition. 



62 



Bibliography 



[1] Comptes Rendus 5" C.G.P.M.. pp. 27-33 (1913); Travaux et Memoires B.I.P.M. 16 (1917). 
[2] Bonhoure. A.. Kilogrammes prototypes, Travaux et Memoires B.I.P.M. 22 (3). 82 pages 
(1966). 

[3] Bonhoure, A.. Note sur refficacite de quelques precedes de nettoyage des poids en 

platine iridic, Proces-Verbaux C.I.P.M. 20, pp. 171-178 (1946). 
[4] Comptes Rendus W C.G.P.M.. pp. 51-53 (1954). 

[5] Marek. W.-J., Pesees, Travaux et Memoires B.I.P.M. 1. pp. D53-D58 (1881) (Description 
of the Rueprecht balance No. 1). 

Thiesen, M., Comparaison des prototypes nationaux avec le prototype international 
^, Travaux et Memoires B.I.P.M. 9, pp. 7-12 (1898) (Description of the Bunge 
balance). 

[6] Guillaume, Ch.-Ed.. Determination du volume du Kilogramme d"eau (Methode des con- 
tacts, Travaux et Memoires B.I.P.M. 14, 276 pages (1910). 

Chappuis, P., Determination du volume du Kilogramme d'eau (Premiere methode 

interferentieUe), Travaux et Memoires B.I.P.M. 14,164 pages (1910). 

[7] Mace de Lepinay, J., Buisson, H.. and Benoit, J.-R., Determination du volume du Kilo- 
gramme d'eau (Seconde methode interferentieUe), Travaux et Memoires B.I.P.M. 14, 
128 pages (1910) (Modifications of the Rueprecht balance No. 1, pp. 33-35). 
[8] Guillaume, Ch.-Ed., La creation du B.I.P.M. et son oeuvre, Gauthier-Villars, Paris, pp. 
240-258(1927). 

[9] Chappuis, P., Dilatation de I'eau. Travaux et Memoires B.I.P.M. 13, 40 pages (1907). 
[10] Broch, O. J.. Poids du htre d'air atmospherique, Travaux et Memoires B.I.P.M. 1, pp. 
A.49-A.58(1881). 

[11] Girard, G. and Menache, M., Variation de la masse volumique de I'eau en fonction de sa 
composition isotopique, Metrologia 7, No. 3, pp. 83-87 (1971) and Recueii de Travaux 
du B.I.P.M. 3, article 13(1971-1972). 

[12] Aimer, H. E., National Bureau of Standards one kilogram balance NBS No. 2. J. Res. 
Nat. Bur. Stand. (U.S.) 76C, No. 1, pp. 1-10 (1972). 



63 



I -1^ 



CHAPTER III 



LENGTH 



One of the principal reasons for creating the BIPM was the unification 
of length measurements. Considerable work was therefore devoted to the 
study of the prototype metres and means for comparing them among them- 
selves with the best possible precision. This work resulted in the 1889 
definition of the metre, based on the international metre identified by the 
symbol^. For almost three quarters of a century, all length measurements 
made at the BIPM and in many parts of the world used ^ as the starting 
point. At the BIPM during this time, the methods of comparison of proto- 
type metres^ were continually improved, less costly alloys were studied for 
the construction of divided scales, the expansion properties of prototype 
metres and of scales were determined, and methods were developed for the 
measurement of geodetic wires, end standards, and industrial gages. 

In 1895, measurement of the wavelengths of several cadmium radia- 
tion lines ushered in a new era. Monochromatic^ optical radiations were in 
fact often used for measuring end-standards by interferometry, and one of 
them was considered as a transfer device for^. Studies of these radiations 
were uninterruptedly pursued at the BIPM as well as at other laboratories 
and resulted in the 1960 definition of the metre based on the orange 
line of krypton 86. Since then, all length measurements must be based 
on this new standard. This involves major modification of apparatus 
for measuring material standards, notably scales and geodetic wires. The 
adoption of the new length standard has not slowed the research on 
monochromatic radiations, indeed, to the contrary. It is necessary to study 
carefully not only the standard radiation itself, its properties and conditions 
of production, but also other radiations capable of being used jointly with 
it, in particular laser radiations which will undoubtedly furnish the basis of 
a new definition of the metre in the near future. 



' In this chapter, a platinum-iridium standard of 1 m nominal length is called prototype metre 
or metre; a length standard with graduation lines is called a divided scale or scale, and such a 
standard of nominal 1 m length is called a metre scale. 

^ These luminous radiations of simple color appear in a spectroscope as narrow lines. In the 
limit, these are pure sinusoidal waves characterized by their wavelengths in vacuo, or by their 
frequencies. 



65 



Measurements of Length Based on the International Metre 

Prototype Metres [7] 

In 1889, the 1st CGPM ratified "the prototype of the metre chosen by 
the International Committee" and declared: "This prototype will hence- 
forth represent, at the temperature of mehing ice, the metric unit of 
length." The CGPM thus implicitly defined the metre. ^ This prototype, the 
International Metre ((iJS), has been preserved at the BIPM since that time. 

Thirty metres have been constructed. Like they have the X cross 
section calculated by Tresca (fig. 1) and are constituted of an alloy of 
platinum (90%) and iridium (10%). They have been carefully compared 
among themselves and with iH, and their expansibility has been deter- 
mined. Thus these metres, distributed at the time of the 1st CGPM to the 
countries requesting them, comprised a consistent set of national stand- 
ards and defined in each country the same length unit with a precision very 
largely sufficient. The BIPM itself acquired several of them as working 
prototypes. 

To assure the permanence of the uniformity thus realized, the Metre 
Convention prescribed periodic verifications of the set of national metres. 

The first verification, starting in 1921, lasted some 15 years. Indeed, it 
greatly surpassed the goal of a simple verification and provoked a set of 
studies whose results considerably advanced the metrology of length. Of 
special note, it instigated a new determination of the expansion coefficients 
of the prototype metres. This determination required extremely lengthy 
studies: the definitive results were finally published only in 1940. 

No other systematic verification of the set of metres has been or- 
ganized since, but numerous national metres have been individually 
verified by comparison with the working prototypes of the BIPM, them- 
selves verified relative to JR. 

The platinum-iridium alloy has fully justified the hopes put in it, from 
the point of view of its stability and inalterability, and the X section was 
certainly the best for excellent rigidity and economy of material; the efforts 
of the BIPM have therefore been directed especially toward improving the 
engraved lines as well as the flatness and polish of the surfaces carrying 
these lines. Progress has been constant. Although in the last century one 
had to reduce the polished surfaces to two small patches of 8 mm length at 



^This definition was made precise by the 7th CGPM, in 1927, in the following terms: "The 
unit of length is the metre, defined by the distance at 0°. of the centers of two lateral lines en- 
graved on the bar of platinum iridium deposited at the International Bureau of Weights and 
Measures, and declared the prototype of the metre by the First General Conference for 
Weights and Measures, this scale subject to standard atmospheric pressure and supported by 
two rollers of at least a centimetre in diameter placed symmetrically in the same horizontal 
plane at a distance of 571 mm from one another." 

66 



Fifiure 1. One end of llic Intri iiat ional Metre. We see the shape nl the eniss section, inseita- 
l)le in a s([uare haviiifi 200 iiiin sides, and tlie 3 lines en<rra\cd (in a polished ""pateh" in llie 
|ilane ol the neulral lihers. The dislanee hetween the middle line and the analogous line on 
I he pa I ell at the i il liei end del ined I h<' riiel i e when this pr nl ol \ pc u as a I I he lemperatnre of 
niell in;i ice. I he usef II I poi I ion ol I hese lines is delimited liy I u o loiigil iidiiial lid lie ia I lines. 



each end of the prototype metres, it is now possible, thanks to the joint ex- 
periments of the BIPM and the Geneva Society of Physical Instruments, to 
put a specular poHsh on the entire lenjith of the prototypes. 

The development of a refined technique for dressing the lines after 
grooving has also allowed obtaining lines with sharp straight parallel edges 
(fig. 2) easy to aline with the microscope cross-hairs. Starting in 1937, all 
the working prototypes of the BIPM and many national metres were 
furnished with new lines. 

The distance specified between the support rollers is chosen to 
minimize the shortening of the standard by flexure under its own weight. 



67 




Figure 2. Appearance of lines engraved on a platinuni-iridium prototype: (a) before 
trimming: (b) during trimming: (c) after trimming. The narrow lines are tiie wires of the 
reticle of the micrometer ocular. 





1 



Figure 3. Principle <>{ the comparison of two metre scales, (a) The two microscopes M and M' 
point the two lines of the same scale before (scale R, position 1 ) and after (scale R'. position 
2) the displacement which can be longitudinal (b) or transverse (c). In cases (a) and (b). the 
space required for the instrument is greater than 3 m and the displacement is of the order 
of 1 m; in case (c), the displacement is only some 10 centimetres. 



68 



Scales 



The BIPM has also contributed to studies relating to the construction 
of length standards in metals or alloys less costly than platinum iridium, of 
lower expansion, or capable of being pohshed more easily. 

The systematic study by Ch.-Ed. Guillaume on nickel steels and the 
important discoveries of invar and elinvar to which this study led, made his 
reputation and have largely contributed to the reknown of the BIPM. 

The best standards, as regards the quality of their lines, are steel 
scales covered by a thick electrolytic deposit of nickel. The specular polish 
which is realized on this metal is excellent, and the lines which can be en- 
graved are remarkable. One thus obtains standards of good stabihty, very 
corrosion resistant, and whose lines are very well defined; they are 
generally divided along their entire length. The cross section of these 
scales generally has the form of an H inscribed in a square 24 mm on a side. 
This is less economical of metal than the X section of the platinum-iridium 
prototype metres, but much easier to construct. 

Measuring Instruments 

Two methods can be envisaged for the comparison of two line stan- 
dards (fig. 3). 

In the first, the two standards are placed in a single line with a fixed 
separation. Two fixed microscopes point simultaneously at the correspond- 
ing extremities of the two standards, then, after longitudinal displacement 
of the set of the two standards, they point at their other extremities. This 
method achieves the same observation conditions for the lines of each stan- 
dard but it is seldom employed because of the risk of relative displacement 
of the two standards and the difficulties of controlling their position. 
Furthermore, for metre scales, it requires very bulky longitudinal 
comparators. 

The second method consists in pointing at the two extremities of one 
standard simultaneously with the two microscopes; the two extremities of 
the second standard are then introduced under the microscopes by means 
of either a longitudinal or transverse displacement. This last solution leads 
to transverse comparators of much smaller dimensions. 



Standard Comparators 

The comparators [2] used for measuring metres and metre scales 
were transverse comparators. 

The first one used, the Brunner comparator, was installed in 1879; in 
its primitive form it conforms to what has just been described and did not 



69 



permit observation of the two lines of the same standard under rigorously 
identical conditions. A basic impnjvement which was made in 1938 con- 
sisted of furnishing it with reversible microscopes, that is to say, 
microscopes which can be rotated a half-turn around their optical axis. 

The combination of observations of the standard in the position called 
AB, and in [josition BA after rotating the microscopes, is equivalent in ef- 
fect to an interchange of the microscopes. 

To point a line is to frame its image between the two lines of the reticle 
in the micrometer ocular of the microscope. Each observer, however, per- 
forms this operation in a different way: in not framing the line in a 
completely symmetric way, he commits an error called the error of 
bisection. This error is eliminated if the observer points the line by ap- 
proaching it successively from one side and from the other. 

These two examples, one of which relates to the improvement of the 
apparatus and the other to improvement of the operating procedure, illus- 
trate the perpetual concern of the metrologist: seeking and eliminating 
errors. 

The Brunner comparator was replaced in 1954 by a new standard com- 
parator, directly inspired by the former one. This comparator (fig. 4a) 
rested on its own new foundations to assure perfect stabihty. Standards 
being compared were still immersed in a water bath; constant circulation 
assured good stability and uniformity of temperature. The tube of each 
reversible microscope (fig. 4b) was provided with a sliding sleeve whose 
lower portion, closed by a flat window, was partially immersed during mea- 
surement: the lines of the scales could therefore be pointed despite the mo- 
tion of the water. 

With this comparator, it was possible to measure the difference 
between two metre standards with good lines, with a precision of 0.1 fim. 




Figure 4a. The standard comparator. Diagram of the installation. P. reinforced concrete pil- 
lars supportin<; the microscopes M and M': C. masonry foundation: S. sand layer: B. floor 
isolated from the comparator. 

70 



Expansion Comparator 

This transverse comparator, installed in 1925 and improved since, per- 
mits comparing the lengths of two scales, one held at a fixed temperature 
and the other taken to various temperatures spaced between 0 and 40 °C. 

Under these conditions, the uncertainty of the determination of a coef- 
ficient of mean expansion is about 10"*^ K"'. 

Geodetic Baseline [3] 

The discovery of invar by Ch.-Ed. Guillaume made an important con- 
tribution to the success of the method conceived by the Swede Ed. Jaderin 
for measuring, with the use of a metallic wire under constant tension, the 
geodetic baselines needed for triangulation of land. For the standardization 
of these wires, a first "geodetic baseline" was installed at the BIPM in 
1900. It was replaced in 1925 by a second baseline which underwent an im- 
portant transformation in 1949. 

The 1925 baseline comprised in fact two distinct parts: a baseline with 
microscopes or "primary baseHne," and a reference baseline or "seconda- 
ry baseline." The primary baseline consisted of seven microscopes with 
4 m separations between adjacent ones. The six intervals so defined were 
measured by means of a 4 m invar scale carried by a moving carriage 
rolling along a track. The length of the primary baseline was transferred to 
the reference baseline by means of two 24-metre primary wires. 

In 1949, the primary baseline was equipped with removable 
references. With the references removed, one determines as previously, by 
means of the 4 m scale, the intervals between microscopes and con- 
sequently the distance between the end microscopes. The end references 
are then put in place and pointed with the microscopes: the distance 
between these references is obtained. Comparison of wires with the 
baseline formed by the references gives their lengths. 

The uncertainty in the most common geodetic wires, those of 24 m, 
was about 10 fxm toward 1960. 

Toward the Chang;e of the Definition of the Metre 

As early as 1827. the French physicist J. Babinet asserted that it was 
necessary to look for a length standard in a visible wavelength and not in 
the dimensions of a material object. Optical radiations, however, are far 
from having the simplicity that was then attributed to them: their study 
gave birth to a new science: spectroscopy. 

In 1859. J. C. Maxwell had suggested choosing as a natural length 
standard, the wavelength of the yellow line of sodium which is easily 



72 



produced by introducing a little salt of this metal into a flame which is ini- 
tially almost colorless. It was observed, however, that this Hght comprises 
two radiations whose separation is about a thousandth of the mean 
wavelength. 

Later, the green hne of natural mercury was considered. Spec- 
troscopes having become more powerful, it was recognized that this was 
really a complex group of neighborhood radiations covering a range of 
about a ten-thousandth of their mean wavelength. 

Toward 1890, an American physicist, A. A. Michelson, discovered a 
radiation, the red hne of natural cadmium, whose sharpness and reproduci- 
bility were unequalled at the time. In 1892-1893, by means of an inter- 
ferometer which was specially built and shipped to the BIPM, he mea- 
sured, in collaboration with J. R. Benoit, the wavelength of this line relative 
to ^ [4]. Confirmation of his results was obtained in 1906 by means of in- 
terferometric etalons called "Fabry-Perot."'* In dry air at 15 °C, this 
wavelength is 

Xcd = 6 438.469 6 x 10-i"m, 

a value which was confirmed later in various repetitions. 

By international accord in 1927, it was agreed that the red hne of natu- 
ral cadmium would become the length standard for spectroscopy, the unit 
of length being the angstrom (A) defined by 

\cd = 6 438.469 6 A 

Thus wavelengths expressed in angstriims would not be affected in case a 
new determination of A.cd relative to the metre should give a slightly dif- 
ferent result. 

At the BIPM, we did not wait for the definition of the angstriim before 
using wavelengths for length measurement. Even before J. R. Benoit and 
Ch.-Ed. Guillaume had made the first attempts to measure the wavelength 
of the "soda light" in 1884, H. Fizeau had constructed in 1880 an apparatus 
using the interference of light for measurements of expansion. An improve- 
ment on this dilatometer in 1882 allowed making these measurements in 
vacuo. This apparatus was used on some samples to determine the expan- 
sion coefficient of the prototype metres [5]. 

Interferometric methods are particularly well adapted to the measure- 
ment of small length variations and to the measurement of small flat-end 
standards because the comparison of these standards to line standards is 
much more difficult. These methods permit direct measurement of the 



* The term '"Fabry-Perot etalon" applies to a set of two parallel semi-transparent mirrors fixed 
to the extremities of a very stable structure (a tube or U-shaped channel of invar). Lif;ht which 
enters the etalon along its axis is subjected to multiple reflections which give rise to particular 
interference phenomena. 



73 



distance between the free face of such a standard and the plane which is in 
contact with the other face of the standard, whether the standard adheres 
to the plane or is simply placed thereon. 

With the use of gages with parallel flat ends beginning to expand in in- 
dustry, A. Perard constructed for their measurement, in 1920, a first spe- 
cial interferometer using Fizeau fringes (see fig. 11 (a)) and, 3 years later, a 
second interferometer, similar in principle but allowing the measurement 
of gages of very great length [6]. This apparatus remained in service until 
1971. 

As early as 1925, the Michelson interferometer was used at the BIPM 
for measuring the length and refractive index of six quartz etalons of 10, 20, 
30, 40, 50, and 100 mm, which were transfer devices for^. 

The utilization of interferometric methods involved the detailed study 
of corrections appropriate to these methods, notably the correction for the 
refractive index of air, permitting the calculation of the true wavelength of 
a radiation under the conditions of measurement as a function of those con- 
ditions (temperature, pressure, humidity) and of the accepted wavelength 
under reference conditions (for example 15 °C, standard atmospheric pres- 
sure, dry air). 

This utilization also involved thorough study of the metrological quali- 
ties of the radiations themselves. A. Perard began a systematic study of the 
radiations of cadmium, mercury, helium, neon, krypton, zinc, and thallium 
in 1921 [7]. He showed that the wavelength of each radiation studied 
seemed to vary slightly when different distances were used for the mea- 
surement. This effect, which was quite predictable for the blue and green 
lines of cadmium and for the mercury radiations, which were known to be 
complex, appeared also for the red line of cadmium, although in a lesser 
degree. It was natural for A. Perard to oppose the adoption of this line as 
the basis for a new definition of the metre after he had thus proved its 
complexity. 

The physical causes of the complexity of optical radiations have since 
been discovered. On the one hand, a natural element is generally a mixture 
of several isotopes whose lines do not coincide exactly. The red line of cad- 
mium appeared simple by a fortuitous coincidence. On the other hand, the 
magnetic properties of the atomic nuclei of certain isotopes confer on their 
emitted radiations a structure called hyperfine. The ideal standard could 
thus be found only among the radiations of a pure (or mononuclidic) isotope 
whose nucleus is free of magnetism. Theory predicts that such a 
mononuclide must have an even atomic number Z and an even mass 
number. 

Radiations actually produced always have a spectral width much 
greater than their natural width. The principal reason is the Doppler effect: 
when an atom is approaching the apparatus used for measuring, the ob- 
served wavelength is diminished; when the atom is receding, the 
wavelength is increased. In a gas. atoms are subject to a thermal agitation 



74 



motion; they emit slightly different radiations according to the component 
of their velocity in the direction of the observer, and the spectral line is 
broadened. This broadening is smaller for heavy atoms whose thermal 
speeds are lower at a given temperature. That ehminates hehum 4 for ex- 
ample, by reason of its small atomic mass, although its atomic number and 
its mass number are both even. One is also interested in choosing an ele- 
ment which can emit a spectrum even at low temperature. 

Toward 1950, a short time after one knew how to separate isotopes, 
three nuclides were proposed by several laboratories (IMM, NBS, PTB) for 
the production of a standard radiation without hyperfine structure: cadmi- 
um 114 (Z = 48), mercury 198 (Z = 80), and krypton 84 or 86 (Z = 36). 

Some studies were necessary for making the choice among these three 
nuclides. 

The BIPM, which had already measured the wavelengths of the yellow 
and green lines of mercury 198 and certain lines of the krypton 84 and 86 
isotopes, then pursued its studies with the use of the Michelson inter- 
ferometer, an apparatus continuously in service and to which several im- 
provements had been made successively, notably the replacement of visual 
observations by photoelectric sensing [8]. 

Thus not only the wavelengths but also the spectral profiles (see p. 89) 
of various radiations were determined. At the time of the second meeting 
of the CCDM (1957), the BIPM could indicate the resuhs of its measure- 
ments of the "half-width" of the red line of cadmium 114, of the green line 
of mercury 198, and of the orange line of krypton 86. 

The conclusion of this work and similar studies made in other labora- 
tories was that the choice should fall on the sharpest of the three lines: the 
orange line of krypton 86. This could be produced with a minimum pertur- 
bation, measurable by other means, in a cold-cathode discharge lamp (fig. 
5) whose capillary is chilled to the temperature of the triple point of 
nitrogen (63.15 K or — 210 °C); furthermore, it suffers little from self-ab- 
sorption which would distort its profile, and its luminance is sufficient. 

The CCDM had recommended that the wavelength of the radiation 
chosen be measured by comparison with that of the red line of natural cad- 
mium produced in a Michelson lamp conforming to international specifica- 
tions, and that a formula established by Edlen [9] be used to go from the 
wavelength in air to the wavelength in vacuo. 

Such are the elements that served to fix the numerical value of the 
new definition of the metre ratified by the 11th CGPM on October 14, 1960, 
in the following terms: 

"The metre is the length equal to 1 650 763.73 wavelengths in vacuum 
of the radiation corresponding to the transition between the levels 2pio and 
5d5 of the krypton-86 atom."^ 

^ The energy levels of the krypton-86 atom which occur in this definition are specified accord- 
ing to the semi-empirical designations used by Paschen as early as 1917. 



75 




Figure 5. Krypt()n-86 lamp in its cryostat. A. anode; C. catlmde heated by an electric current. 
The lamp Kr is immersed in liquid nitrogen contained in the Dewar flask D. The whole is in 
an airtight chamber in which there is a partial vacuum for obtaining the triple point of 
nitrogen ( — 210 °C). The krypton pressure is the vapor pressure of solid krypton at this tem- 
perature. The capillary tube T has a length of about 7 cm and an inside diameter of about 2 
mm: the electric current density is adjusted to 0.3 A/cm-. Under these conditions, the 
orange radiation emitted in the direction of the arrow has a wavelength equal to that which 
corresponds to the definition of the metre within 1 in lO**. 



76 



This definition has been completed by a Recommendation of the 
CIPM which specifies the characteristics of the discharge lamp producing 
the standard radiation [10]. The (rounded) value of the wavelength of this 
radiation is: 

\=1 m/1 650 763.73 = 0.605 780 211 ^tm. 



Putting the 1960 Definition of the Metre Into Practice 

The adoption of a new primary standard of length did not diminish the 
interest in material standards of length, scales, gage blocks, and geodetic 
wires; but since then it has been necessary to measure these as directly as 
possible by comparison with the wavelength of the standard radiation of 
krypton 86. There were progressively put into service a photoelectric inter- 
ferometric comparator for measuring divided scales and long gage blocks, 
an interferometer for measuring gage blocks up to 250 mm in length, and 
an interferometric method for measuring the geodetic baseline. 

Photoelectric Interferometric Comparator 

Starting in 1952, the BIPM studied, in collaboration with the construc- 
tor, a design for a comparator using photoelectric microscopes. These 
microscopes of a new type had already been proven as essential com- 
ponents of a dividing engine and also in a comparator for calibrating di- 
vided scales. The design was improved over several years; the new com- 
parator should permit not only comparisons of scales and calibration of 
their subdivisions, but also the measurement of ruled scales and end stan- 
dards up to 1 m long by comparison with wavelengths of optical radiations. 
The comparator was installed in 1961 in a specially fitted-out room; it was 
put in service in 1964 [11] after installation of devices for ancillary mea- 
surements (measurements of refractive index and temperature of the air), 
and putting the photoelectric microscopes into working order. A device 
called a fringe-counter was adapted to the comparator in 1969 [12] . 

The comparator must be shielded from temperature variations which 
would change its own dimensions and those of the standards being mea- 
sured, and from variations of atmospheric pressure, which would change 
the refractive index of the air and consequently the wavelengths of the opti- 
cal radiations used as references; it must also be protected from ground 
vibrations, which would disturb its operation and the observation of inter- 
ference fringes. For this, it is enclosed in an air-tight isolating tank of 25 m^ 
volume mounted on a reinforced 40 Mg platform resting on a dozen 
concrete pillars. We have achieved an anti-vibration suspension by inter- 
spersing between the platform and each pillar a set of heUcal springs and 



77 




I I I 

0 1 2m 

Figure 6. Overall plan of the nidiii tor the photoelectric interferometric comparator. S,. air- 
conditioned part; Sa. control room; C. tank bedded on its anti-vibration platform, and con- 
taining; the c(jmparator C" and the refractometer R; P, control and measurement console; 
Pi. P2. pillars mounted on the platform, particularly used for supporting light sources; M, 
const)le of comparator motors, mounted on the platform, and used to support the exit 
telescope of the interferometer; H, H". ports for the entry and exit of light beams. For more 
details on the optical lay-out, see figure 9. 



78 



a damping device filled with silicone oil. The room (fig. 6) is divided into 
two parts by an isolating partition. Access to the part containing the com- 
parator can be had only outside the time of measurement and, of course, 
the tank is entered only for placement of the standards under study. This 
part of the room is held at a constant temperature, generally 20 °C, to 
within about 0.1 °C. The light source, comparator motors, control console 
for the various moving parts of the comparator, and the display of data from 
the photoelectric microscopes are grouped in the second part of the room, 
occupied by the operators during measurement. 

The photoelectric microscopes operate on the following principle. A 
rectangular spot (8 /xm wide, approximately the groove width, and of ad- 
justable length, for example 160 /u,m) is projected onto the ruled surface of 
the scale to be measured. The spot explores a small region by an oscillatory 
motion along the direction of the scale. The reflected light is received by a 
photoelectric sensor. If the explored zone carries a groove, the sensor gives 
a signal at each passage of the spot over the groove. When the groove is 
centered on the average position of the spot, these signals are separated by 
equal time intervals, but this is not so if the groove is off center (fig. 7). 
These signals are electronically processed and the position of the groove 
relative to the average spot position as reference is exhibited directly on a 
display device. The resolution of the system is 1 nm for the measuring 
range most commonly used (10 /xm). 




Figure 7. Principle of spotting the position of a line with a photoelectric microscope. Signals 
delivered by the photoelectric sensor in the three following cases: (a) line centered, tt = h: 
(b) line decentered to the right, ('i < t'-,: (c) Hne decentered to the left, > l"-,. The signals 
are produced by the passage of the spot across the line during its movement towards the 
right (signals d) or towards the left (signals g). 



79 



The comparator (fig. 8) comprises two photoelectric microscopes 
whose positions are adjustable along a common longitudinal beam. Two 
1 m standards can be placed end-to-end on the bench which holds the scales. 
They are compared by the scheme indicated in figure 3 (b), that is to say, by 
alternatively pointing the two lines of one, then of the other, by a longitu- 
dinal displacement of the scale bench which is supported on a carriage. 
Naturally, several pointings are made on each standard and its tempera- 
ture is measured. A complete comparison is very time consuming: it 
requires the interchange of standards, turning them end for end. and a half- 
turn rotation of the microscopes about their axes. This method of compar- 
ing metre standards or intervals on a single scale has been abandoned, lit- 
tle by Httle, in favor of interferometric methods; the latter are more rapid 
and especially more precise because they allow direct comparison of the 
length of the standard with the primary standard wavelength of krypton 86. 

The comparison of line-standards of length with wavelengths of optical 
radiations requires the comparator to be equipped with an interferometer 
(fig. 9 (a)). A Michelson interferometer is used here. The parallel beam from 
a monochromatic source is split into two beams, one of which reflects from 
a fixed mirror, the other from a mirror moving with the scale. The beams 
recombine and produce an interference pattern in the focal plane of the 




Figure 8. Photoelectric interferometric comparator of tiie BIPM. B. scale bciicli: Ch, car- 
riage; C. C. sliders carrying the photoelectric microcopes MP. MP', and whose positions 
are adjustable along the beam P; Mm. mo\ablc mirror linked to the scale: Me. eclipsing 
mirror: IM. splitting and compensating plates of the Michelson interierometer. 



80 



T • ^ 



telescope objective. The illuminance at the center of this pattern varies 
sinusoidally during displacement of the moving mirror; a period of its varia- 
tion (also called a unit variation of the interference order) corresponds to an 
increase in the length of the variable beam equal to the wavelength of the 
radiation used, that is, it corresponds to a mirror displacement of a half 
wavelength. The principle of the measurement is thus very simple. The ini- 
tial position of the scale is chosen such that its origin line is centered ex- 
actly under one of the microscopes; the scale is displaced so that its end 
line is centered under the same microscope. To obtain the length / of the 
scale, equal to the displacement thus made, which is also that of the mova- 
ble mirror, it suffices to know the wavelength of the radiation used and to 
determine the variation p of the interference order; we have, in fact, / = 
pA./2. It is easy to obtain the fractional part of the interference order for the 
initial and final positions of the scale by measuring the illuminance ob- 
tained at the center of the pattern when the length of the variable beam is 
artificially changed by small known amounts. One thus obtains the frac- 
tional part / of the variation of interference order p. Two methods are used 
for determining its integral part e. 

To apply the first, called the method of excess fractions, one uses 
several radiations of well known wavelengths, Ai, As ... and one mea- 
sures the corresponding fractional parts f\,fz,fi The integral parts ei, 

e-i, es .... are not known exactly, but from the fact that one must have l — {ei 

+f) XJ2 = (62 +fi) W2 = (ei! +f,) \3/2 = and that / is known in 

advance to a few micrometres, or even closer, one of the integral parts, say 
ei, can be predicted to within 10 units. Then / has 20 possible values, regu- 
larly spaced. To each of these corresponds a ca/c«/a?ea? value^',^', . . . . 

which is compared with the observed value /j, /s If the wavelengths 

used have been well chosen, a single set of calculated values coincides with 
the set of observed values within the Umit of measurement error. The cor- 
responding value of / is the value sought. This method is very reliable with 
four radiations for the measurement of intervals up to 600 mm. Above that, 
the determination of fractional parts becomes too uncertain, even impossi- 
ble with ordinary optical radiations, by reason of the rapid diminution of 
the visibility of the interference due to the necessary increase of path dif- 
ference (see p. 91). For a 1-m scale to be measured in this way, it must have 
a Hne near the middle: its two halves are then measured successively. 

The second method consists in counting the cycles of variation of illu- 
minance at the center of the interference pattern, that is to say, the inter- 
ference fringes which march through this point. This method had already 
been used at the BIPM very long ago in 1892 to measure the wavelength of 
the cadmium red line. At that time, interference patterns were observed 
visually; counting some thousands of fringes, corresponding to a length 
measurement of the order of a millimetre, constituted a formidable task. 
This method has been restored to respectabihty thanks to the exceptional 
properties of lasers (see p. 92 ). The extreme sharpness of laser hues allows 



81 




Figure 9. Optical system of the three interferometric arrangements used on the comparator, 
(a) Michelson interferometer illumiriated by the krypton lamp or by the laser; (b) fringe 
counter for use with the laser; (c) refractometer (krypton lamp or laser); the vacuum 
chamber, which can be placed in beam 1 or in beam 2; is not indicated. 

C, entrance collimator; D. rotary diffuser; F, interference filters allowing separation of 
certain lines emitted by the lamp Kr (krypton 86); L, laser; Me, eclipsing mirror; Mf, fixed 
mirror; Mn, movable mirror; P, refractometer photomultiplier, Qk, section of the beam 
falling on the four sensors; Qs, section of the beam observed at the interferometer exit; R, 
array of four sensors; S, exit telescope; Tf, fixed corner reflector: Tm. movable corner 
reflector. 



82 



obtaining interference without appreciable loss of visibility for all path dif- 
ferences usable in the laboratory. The intensity of laser rays and the use of 
photoelectric sensors make rapid electronic counting feasible. The device 
installed on our comparator allows counting at about 6 mm/s maximum 
speed of translation of the carriage. The counting of about 3 160 000 
fringes, corresponding to a length of 1 m, is thus carried out at a rate of 
19 000 fringes per second. To achieve this performance, we had to add a 
corner-reflector interferometer to the plane-mirror interferometer (fig. 9 
(b)) to maintain proper behavior despite the small defects in the movement 
of translation. The beam is split among four quadrants by means of retarda- 
tion plates on one of the surfaces of the stationary corner reflector; these 
plates are arranged so that the path differences in successive quadrants 
are D, D + A./4, D + A/2, D + 3X/4. A sensor is associated with each 
quadrant. Then the signals from two adjacent sensors are in phase quadra- 
ture; those from opposite sensors are in phase opposition. By associating 
these latter signals with two differential ampUfiers, the two quadrature 
signals needed for reversible electronic counting are available. 

The speed of this method is particularly important for the calibration 
of divided scales. 

The two methods which have just been described are also applicable 
to the measurement of flat-end gages. A gage adhering to a base plane con- 
stitutes a system of two mirrors (this plane and the free face of the gage) 
whose separation is the length of the gage. In the method of excess frac- 
tions, these two mirrors play the same role as the initial and final positions 
of the mirror Mm in the case of scale measurement (fig. 10 (a)). Measure- 
ment of the fractional parts corresponding to the plane or to the free face 
are made by selecting one or the other by means of diaphragms suitably 
located in the beam. In the fringe counting method (fig. 10 (b)), these two 
mirrors play the same role as the ruHngs on the scale, and the image of the 
fixed plane mirror given by the splitter plays the role of the microscope. A 
displacement equal to the length of the gage is realized by successively 
placing these two mirrors in the position of the image of the fixed mirror; in 
the neighborhood of this position, the coincidence can be adjusted by ob- 
servation of the characteristic white light interference. 

The comparator operates in air which is near atmospheric pressure. 
The wavelength to be used in the formula / = p\/2 must be derived from the 
vacuum wavelength and the refractive index, n, of air by the relation k — 
Kn. The definition of the metre in fact furnishes the vacuum wavelength of 
krypton 86; the wavelengths of other radiations used are deduced from this 
by comparison in vacuo. The index n is measured inside the tank by means 
of a refractometer (fig. 9 (c)). For the value obtained to indeed be that of the 
index of the air traversed by the beams of the main interferometer, it is 



83 



I L- 



/ 
MP 



Mm 



iMf 



B 

D 



,Mf' 



-/ 



Mf 



|Dl 
I 

ID2 
I 



I 




MP-^T 



MP 




Tm 



Mf 



Tm 




Mf 



Figure 10. Analogy between measurement of a scale and measurement of a gage-block, (a) 
Measurement of a scale by the method of excess fractions, or static measurement of a gage- 
block. The displacement which causes the lines T and T" to be centered under the 
photoelectric microscope MP successively, is equal to the length / of the scale. The 
distance between the initial and final positions of the mirror Mm. linked to the scale, is 
measured by means of interpolation ot interference fringes obtained with several radiations 
for each of these positions (in addition to that, we know that the positions are symmetric 
about Mf', the image of the fixed mirror of the interferometer). The free face C of the gage- 
block, and its base plane B, i)lay the same role as the two positions of Mm. Measurement of 
the distance requires successive use of two diaphragms Di and D2 to limit the useful beams 
although only one, Di is used for the scale, (b) Measurement of a scale or of a gage-block by 
fringe counting. The translation of the scale is the same as before. The displacement of the 
movable corner reflector Tm, linked to the scale, is measured by counting interference 
fringes using laser radiation. The base plane B of the gage-block and its free face C play the 
same role as the scale lines T and T" but they cannot be pointed with the microscope MP: 
to place them successively in the same position, they are made to coincide with Mf", the 
image of the fixed interferometer mirror. Tlie displacement of the corner reflector Tm', 
linked to the gage-block, is equal to the length of the latter and is measured by counting 
fringes as in the case of the scale. 



84 



necessary that conditions, especially pressure, be the same for the two ap- 
paratuses; in particular, they must be in the same horizontal plane. This 
refractometer is itself a small interferometer comprising a vacuum 
chamber of known length which is placed in one beam, then in the 
other. The index of refraction is derived from the difference between the 
interference orders corresponding to these two positions. 

The result of the measurement of a standard, scale, or gage, is always 
adjusted to a reference temperature, for example 20 °C. For this, it is 
necessary to know the exact temperature of the standard at the moment of 
measurement, and also its coefficient of expansion. The temperature mea- 
surement is made in two steps: a platinum resistance thermometer gives 
the temperature of a copper reference block located inside the tank, and 
thermocouples give the temperature difference between the block and the 
standard itself. The accuracy of this measurement is 0.001 °C. As for the 
coefficient of expansion, this is determined by measuring the length of the 
standard at various temperatures over a range of several degrees on each 
side of the reference temperature; the uncertainty of this coefficient does 
not exceeds X lO'-'K"'. 

The uncertainty in the length of a standard at its reference tempera- 
ture is largely due to the quality of the standard itself: quality of the rulings 
and flatness of the ruled surface, for a scale; flatness and parallelism of the 
faces, for a gage block. The uncertainty is generally several hundredths of 
a micrometre. 

Since this comparator was put in service, numerous standards have 
been measured, including 10 national metres and the 4 working prototype 
metres of the BIPM. These latter, already known relative to ^M, thus are 
also known relative to the new definition of the metre. From this is deduced 
the difference between the ''1889 metre" and the "1960 metre." The result 
obtained has been verified by direct measurement of ^ against the stan- 
dard radiation. This difference, which is 0.25 /xm (the current metre being 
the shorter one) is without practical consequence. 

Interferometer for Measuring Gages 

In 1971, the BIPM acquired an interferometer for measuring gage 
blocks. This commercial instrument replaced the Fizeau-fringe inter- 
ferometer which had been in use since 1923. Fizeau fringes are formed 
between two nearly parallel plane mirrors and are observed through one of 
them which is semi-transparent; these are fringes of equal width. In mea- 
suring a gage block (fig. 11 (a)), the length of the air path above the base 
plane is necessarily longer than that above the free face. This results in a 
fringe system observed on the base plane which has less contrast than that 
seen on the free face. This reduction of contrast limits the length of gages 



85 



R 



1/ 
i B 




Figure 11. Static measurement of jiage-blocks. (a) With a Fizeau interferometer, (b) With a 
Michelson interferometer. 

The measurement ^)t ihc lfii;^lh / resuhs from interpolatinjt the ei[ual width frinj;es which 
are formed between the reference plane R (semi-transparent mirror) or R" (image of a fixed 
mirror) and, on the other hand, the free face C of the gage-block or its base plane B. (c) 
Appearance of the fringes observed in case (b). The interpolation consists in locating the 
position of a fringe given by C in relation In the two fringes, given by B. which enclose it. 
The excess fraction here is c//c/,,. 



Mn 



M 



A 

-n- 



o: 



6 



v 

^---/- 
> 



Mm 



24 



Mml 



Mf 



a 



-i-F 

o 
Kr 



Figure 12. Plan of the arrangement for interfert)metric measurement of the 24-metre geodetic 
baseline. A, B, Fabry-Perot etalons nf 0.2.S m and 1 in: F. interference filters permitting the 
selection of certain radiati(ms fidin the lain|) Kr (krypldii 86). for the measurement of A 
(mirror R:i in its lower position): S|. helium-neon laser, and S). point source, used for tlie ad- 
justments; Si, white-light xenon source used for optical multiplication by 4 (Ri and Ris in 
their upper positions. R> in its lower position) and by 12 (Ri in its lower position, R2 and R.-) 
in upper position. A ecliiised): tiie movable mirror Mm is then alined with microscope Moor 
Mj4. and the line T. engraved on the lower edge of the mirror, can be pointed: Mf, fixed mir- 
ror: (). ()|. (),. 0 . objectives: 1-. observation telescope: R. orientable mirror: IM, splitting 
and roinpi ii'ialiiig |)lates of the Michelson interferometer. 



86 



measurable by this procedure to about 100 millimetres. Furthermore, the 
Fizeau fringes are slightly asymmetric. 

The new instrument uses a Michelson interferometer. These fringes 
are also formed between two mirrors, but one of these is virtual; it is the 
image of a fixed mirror. It can therefore be placed at the midpoint of the 
gage (fig. 11 (b)).The two sets of fringes have equal contrast and the length 
of gages which can be measured is doubled (it is about 200 mm with a natu- 
ral cadmium source and 250 mm with a mercury-198 source). In addition, 
the fringes are symmetric. In short, the arrangement is the same as for the 
measurement of gages with the interferometric photoelectric comparator 
by the method of excess fractions (see p. 81). The temperature is deter- 
mined in the same way; the refractive index of the air is measured with a 
built-in refractometer, or calculated from ambient conditions. On the other 
hand, the determination of the fractional parts of the interference order is 
made in this case by visual observation (fig. 11 (c)). The details of construc- 
tion make the use of this instrument simple and fast. Thus, for example, a 
rotating carriage can hold up to nine gages, each wrung onto the base 
plane. The desired gage can be brought to the measuring position by exter- 
nal control. 

The uncertainty of the measurement is generally 0.01 to 0.04 fim, de- 
pending on the length of the gage. 

Interferometric Measurem en t of the Geodetic Baseline 

This installation (fig. 12), completed in 1964, concerns only the inter- 
ferometric measurement of the distance between the axes of the 
microscopes Md and M24, 24 metres apart. The passage from this distance 
to that which separates the corresponding references, and the comparison 
of geodetic wires with the baseline established by these references, remain 
the same as described earlier (see p. 72 ). 

Counting fringes would without doubt be appHcable as a method, but 
there would be serious difficulties due to the considerable number of 
fringes to be counted in a reasonable time (more than 75 000 000 with visi- 
ble radiation), and to the necessity of realizing a high-quality motion of 
translation. An original method has been developed [13]; it is based on the 
principle of optical multiphcation and uses Fabry-Perot etalons. 

Monochromatic radiation which enters a Fabry-Perot etalon along its 
axis gives rise to narrow circular fringes observable with a telescope. By 
measurement of the angular diameters of a few of the rings for several 
radiations of known wavelength, the distance between the two mirrors of 
the etalon can be determined by the method of excess fractions. 

In this way, the exact length /o of a 0.25-metre etalon can be deter- 
mined using several radiations of krypton 86, including the standard radia- 



573-106 0-75-7 



87 



tion. Naturally, the refractive index of air must be known, but this can be 
calculated from ambient conditions. 

Now let there be a second etaion whose length li is close to a multiple 
of the length of the first one, for example, a 1 -metre etaion. By illuminating 
the system of these two etalons in line with an intense source of white light, 
one can observe interference patterns. These can be simply explained by 
saying that a beam which makes a round trip in the 1-m etaion travels about 
the same distance as the beam which makes four round trips in the 0.25-m 
etaion. These two beams give an interference pattern whose appearance 
depends only slightly on the wavelength and remains visible with a light as 
complex as white light. Many other beams of appreciable intensity are also 
present. Some of these produce interference, others do not but contribute 
to a lessening of the fringe contrast which is therefore decreased when the 
length ratio of the two etalons is increased. A method based on the dis- 
placement of the interference fringes when the orientation of one etaion is 
changed slightly permits determination of the small difference /i — 4/o. 
The length /j is thus obtained. 

Quite analogous phenomena are produced by observing, through a 1- 
metre etaion, the light from a Michelson interferometer whose path dif- 
ference of the two arms is a multiple of /j. In particular one can obtain 
rigorous multiplication by 12 for 2 positions of the movable mirror of the 
Michelson interferometer: in one, the variable arm is shorter than the fixed 
arm by 12 /i; in the other, it is larger by 12 /]. To go from one of these posi- 
tions to the other requires a 24 /i displacement of the movable mirror. The 
installation is such that one of these positions is plumb with the microscope 
Mo, and the other with M24. By pointing each microscope on a line engraved 
on the edge of the mirror, the distance between their axes is obtained. 

The method described above is also suitable for measuring the 
distance between any two of the microscopes located between Mo and M24, 
since this distance is always a multiple of 1 m. 

Putting this into operation allowed appreciable progress, notably for 
the measurement of geodetic tapes observed directly with the 
microscopes; in fact the determination of the 24-metre distance between 
microscopes Mo and M24 is now carried out to an estimated 2 or 3 fxm. 

Complementary Studies of the Standard Radiation 

The accuracy of interferometric length measurements is most often 
limited by instrumental imperfections: defects of mirror flatness, expan- 
sion, drift, etc. These limitations correspond to imperfect utilization of the 
possibilities offered by monochromatic radiation. Errors due to instrumen- 
tal defects have been studied at the BIPM since its creation. We most often 
know how to eUminate their effects or how to allow for them by appropriate 
corrections. 

88 



I 



With the 1960 definition of the metre, it became essential to study the 
Hmitations due to the radiation itself: a krypton lamp always gives an im- 
perfect realization of the length unit. 

Extrapolation to the Unperturbed Atom 

The definition of the metre refers to an atom of krypton 86 which is not 
perturbed, therefore isolated and stationary. In a spectral lamp, one must 
take account of several effects which influence the emitted radiation: ef- 
fect of pressure due to interactions between atoms, Doppler effect due to 
thermal agitation of atoms or their entrainment by the exciting electric 
current. Thermal agitation betrays itself by a practically symmetrical 
broadening of the spectral profile, without displacement of the mean 
wavelength. On the other hand, one must extrapolate to zero pressure and 
current to evaluate the effects of pressure and current on the wavenumber** 
of the emitted radiation (fig. 13).When the krypton-86 lamp is used under 
the recommended conditions ( p. 76 ), these effects compensate each 
other and the wavelength of the emitted radiation (fig. 13) corresponds 
to that of the definition of the metre to better than 1 in 10**. 

Spectral Profile 

The broadening of the spectral profile is mainly due to the Doppler ef- 
fect from thermal agitation. When the lamp is used under the recom- 
mended conditions, the half-width of the spectral profile, in terms of 
wavenumber, is around 8or=1.3 m~' (fig. 14). This broadening limits the 
visibility of the interference fringes for large path differences. In a Michel- 
son interferometer, the visibility of the fringes of the standard radiation is 
no more than about 0.01 at a path difference of Z) = 0.9 m (fig. 15); it is still 
less for the other usual radiations (lasers excepted). It is thus practically 
impossible to measure directly lengths greater than 1 m with the standard 
radiation itself. 

A more complete study [16], in which account must be taken of inten- 
sity fluctuations, shows that the relative precision of interferometric mea- 
surements reaches a maximum of the order of 10'' for lengths of the order 
of 0.4 metre (fig. 16). 

We have also been able to demonstrate a very small asymmetry of the 
spectral profile [15] whose origin is still unexplained. In interferometry, 
this asymmetry betrays itself, in principle, by a relative variation of the 



*To describe the spectral properties of a radiation, it is preferable to use the wavenumber a 
or the frequency/ which are related to the wavelength X and the speed of light in vacuum by 
the relations: o-=l/A=//c. 



89 



A cr 



,75 



1650763,73 



m 



-1 



,70 




© 



58 



"I 
61 



4 Pa 



63K 



Figure 13. Extrapolation to zero pressure in a i<rypton-86 lamp [14]. The pressure p in the 
lamp is the saturated vapor pressure of solid krypton at temperature T: it is controlled by 
chan<;ing T. The current density is held at 0.33 A/cm-. The wavenumber cr of the emitted 
radiation depends on the pressure and on the direction of observation. Curve (1): observer 
at the cathode end (lijilit emitted in the current direction). Curve (2): observer at the anode 
end (light emitted in the direction opposite to the current). 

By taking the average (straiglit line (3)). one eliminates the Doppler effect responsible for 
the difference between curves (1) and (2). The value of the wavenumber extrapolated to zero 
pressure corresponds, to better than 1 X 10 to that obtained at r=63.15 K (triple point 
of nitrogen) at the anode end (curve (2)). 

Under different conditions, one obtains lines like (4) (current density. 0.78 A/cm^) or (5) 
(transverse observation) which allow placing the value 1 650 763.73 m ' on the cr scale. 



90 



1650 763,73 m-^ 

Figure 14. Spectral profile <if the standard radiaticm [15]. The standard radiation is emitted 
by a krypton-86 lamp operating under recommended conditions. The spectral profile is 
deduced from the variation in the visibihty of interference as a function of path difference 
in a Michelson interferometer. The lack of symmetry is imperceptible. The ordinate at the 
peak is taken as unity. 




Figure 15. Variation of the visibiUty Fof interference as a function of path difference Z) in a 
symmetrical Michelson interferometer, for the standard radiation. 

F is defined (Michelson) in terms of the maximum ly, and minimum /,„ intensities of the 
fringes, by 



hQ 




D 



Figure 16. Variation of the relative precision of measurement as a function of path difference 
D. In measuring a length / (or a variation of interference order Ap = AZ>/X) it is always 
desirable to use the path difference variation AD = / between Di = — Ij'Z and 0-2=+ 112. In 
this case the precision is characterized by Q= l/Sl, 81 being the uncertainty in /. The scales 
are arbitrary. For small path differences the interference visibility varies little and Q 
increases with D: for large path differences, the reduction of visibility becomes the domi- 
nant effect. 



91 



order of 1 X 10 in the apparent wavelength as a function of path dif- 
ference; it is fortunately without practical consequence: when the max- 
imum precision is used, the apparent wavelength corresponds closely to 
the average of the wavelengths at the peak and center of gravity of the 
spectral profile [17] for whatever type of interferometer used. 

Reproducibility 

To evaluate the reproducibility of the realization of the length stan- 
dard, it is sufficient to compare the wavelengths of the radiations emitted 
by various krypton-86 lamps. The lack of reproducibility is thus evaluated 
to be ±2 X 10"-' [18]. A better check consists in comparing length mea- 
surements in different laboratories, made on an "object" whose stability 
and reproducibility are certainly better than those of the length standard it- 
self. The measurement of wavelengths of stabilized lasers (see p. 98) has 
recently permitted such comparisons. The dispersion of the measurements 
is less than ±4 X lO"''. As this last value includes the inevitable imperfec- 
tions of utilization, it well confirms the preceding evaluation. It appears 
impossible to reduce the uncertainty of measurements using the krypton 
lamp to less than 1 X 10 

Lasers 

Since 1955. the invention of the laser" has brought spectacular 
progress to interferometric procedures. The BIPM has been particularly 
interested in continuously operating helium-neon lasers (fig. 17); only these 
are involved in the following discussions. These laser sources are very 
directional, very intense, and can be very monochromatic. It is especially 
this last property which interests us here: the spectral width Scr of the 
radiation from a laser can be less than 0.001 m"' (6/= 30 kHz), which al- 
lows observation of interferences of perfect contrast at all customary path 
differences and up to several kilometres. 

Unfortunately, although the instantaneous spectral profile is very nar- 
row, the mean wavelength A varies rapidly with time. The mean wavelength 
must be inside the relatively broad spectral band (spectral width of the 
order of 1 GHz, or Acr = 3 m"M in which laser action can occur in the mix- 
ture of helium and neon suitably excited by an electrical discharge. In this 
band, the laser oscillations fix themselves spontaneously to one or several 



' The term laser, whic h has been accepted into numerous languages, is a contraction of ^'light 
amplification by stimulated emission of radiation." Originally the term "laser effect" was ap- 
plied to the phenomenon of amplification of visible waves; usage now attributes the name 
"laser" to light sources using the laser effect. 



92 





Figure 17. Sketch of the principle of a iieliuni-neon laser (X =0.633 /xni). M, M'. slightly 
transparent concave mirrors, forming the resonant cavity: their curvature keeps the ligiit 
beam in the cavity throughout numerous round trips. A. mixture of helium (about 85%) and 
neon (about 15%) under a total pressure of 300 Pa, excited by an electrical discharge; tiiis 
medium amplifies the waves of X = 0.633 /xm which traverse it; the oblique windows 
(Brewster angle) have a negligible reflection factor for light polarized in the plane of the 
figure. F, F'. emerging beams, polarized in the plane of the figure. 



frequencies corresponding to resonances of the cavity: for a cavity of spec- 
tral length L, the resonance frequencies / (for oscillations of axial sym- 
metry) correspond to L = kKl2, whence f= kc 1 2L, where k is an integer. 
Different values of k correspond to different axial modes of oscillation of the 
laser. For a sufficiently short cavity, only a single oscillation mode can be 
excited and the laser is then said to be unimodal; this is the only case with 
which we are concerned. The frequency /remains dependent on the optical 
length of the cavity. Since the cavity contains the optical medium, electri- 
cally excited, the stability of L, hence also that of /, is always mediocre. 

The metrological interest in lasers increased many fold when it was 
learned how to stabilize the frequency (or the wavelength) of the emitted 
radiation by various artifices. 



Stabilized Lasers 

The power radiated by a laser varies as a function of the optical length 
of the cavity, hence as a function of the frequency / For each mode, it has 
a maximum on which is superposed a sHght depression, the Lamb dip, 
under certain excitation conditions (see fig. 19 (a) and p. 97). The maximum 
(or the superposed minimum) is located at a characteristic frequency of the 
amplifying medium. This property is easily used to stabilize the length of 
the laser cavity through feedback, for example by the procedure indicated 
in figure 19 (a) and (d), in such a way that it corresponds to the maximum 
(or minimum) of power. The related variations of wavelength of a laser sta- 
bihzed in this way can be of the order of 1 X 10 *^ for periods of the order of 
several months. Over a longer time, a drift (fig. 18) is usually observed, ap- 
parently due to diffusion of helium through the walls. Several lasers of this 
type are used at the BIPM, for example for length measurement by fringe 
counting; their wavelengths must be calibrated regularly. 

The length of the laser can also be slaved in such a way that the 
emitted wavelength corresponds to a resonance of an auxiliary optical cavi- 



93 



ty [19]. The optical length of the auxihary cavity then determines the 
wavelength of the laser and the stability of one controls the stabiUty of the 
other. Here again, calibration is indispensable and it must be repeated 
periodically. 

A much more effective procedure which we shall discuss in more 
detail consists in forcing coincidence between the frequency of the laser 
and that of a "saturated absorption line." 

A I 




1969 1970 1971 1972 1973 1974 

Figure 18. Change with time of the wavelength of three lieHum-neon lasers locked to the 
Lamb dip of the emission. The wavelength is given in picometres (1 pm = 10"'- m). 



Lasers Locked to a Saturated Absorption LJne 

An absorption cell containing, under low pressure, of the order of 1 Pa. 
a gas which exhibits an absorption line within the Doppler width of the 
laser frequency, is placed in the resonant cavity: for example, a methane 
cell for a helium-neon laser operating at 3.39 /xm. The absorption reduces 
the power emitted by the laser (fig. 19 (b)). 

The gas molecules, at rest, can absorb radiation of frequency/). If the 
laser oscillates at a frequency/ near/i. the waves which propagate along 
the cavity can nevertheless be absorbed by certain molecules of the gas. 
For this to happen, it is sufficient that the velocity of these molecules, due 
to thermal agitation, have a longitudinal component such that, by Doppler 
effect, they "see" a wave of frequency/). If, for example. /is less than/), 
the waves which propagate to the right are absorbed by molecules 
travelling to the left and vice versa: if /is higher than/i. the phenomenon is 
similar under interchange of the roles of the two families of waves. If /=/). 
the two families of waves are absorbed by a single class of molecules: those 
whose velocity is perpendicular to the axis of the laser and for which the 
Doppler effect vanishes. 

When the absorbed radiation is very intense, there is also a 
phenomenon of saturation. Molecules which absorb radiation of frequency 
/remain in an excited state for a certain time. The number of molecules 

94 



I 



® 



I. / ! 




A P 



/f-1 




/A 





G 












DS 




C ^ril R 




DS 



M 









/ 











M 



P ifiure 19. Piinciplf of luckiiiji a laser (\ = 3.39 ixm). (a) Vaiiatidii iif emitted power P as a 
function of cavity length /. A, iielium-neon amplifier tube. R. photoelectric sensor. / — 1. k. 
i + successive modes. Under certain conditions of excitation, the Lamb dip LD is ob- 
served, (b) The same laser witii an absorption cell C containinji methane under a pressure 
of 1 Pa. The emitted power is less. A peak S due to saturated absorption is observed, (c) 
The cavity length / is modulated with a very small amplitude at the frequency F,, by use of 
the generator G and the piezoelectric ceramic PZ. The photoelectric current is modulated 
at the frequency F,. with an amplitude m proportional to the first derivative of P(l). The 
component at frequency F^, is isolated and rectified by a synchronous-detector amplitier 
DS; the output voltage /V/of DS is pro|)ortional to m. If the mean value / of the length / is 
varied. M vanishes at S' which corresponds to the top of the peak S. and varies very rapidly 
in its neighborht)od. (d) M controls a second ceramic PZ' with the help of the amplifier HT. 
If m > 0, PZ' lengthens the cavity: if m < 0. it shortens it. The mean length stabilizes at one 
of the values for which M vanisiies (points S'). corresponding to the top of one of the peaks 
S. 



95 



remaininji in the normal state diminishes, and with this, the capacity of the 
gas to absorb at frequency /: there is saturation of the absorption. 

In the laser cavity, this saturation occurs more readily for molecules 
which can equally absorb waves which propagate to the right or to the left. 
The absorption then decreases when the frequency / of the radiation (a 
function of the cavity length) passes through the value/), and the radiated 
power then presents a "saturated-absorption peak." The molecules 
responsible for this peak being just those for which the Doppler effect 
vanishes, this peak is not broadened by the Doppler effect.** One thus ob- 
tains peaks of width 8/ less than 100 kHz (relative width 1 X 10"") with 
methane at \ ~ 3.39 jxm and less than 3 MHz (relative width 6 X 10"-') with 
iodine at A. = 0.633 ^tm. 

It is relatively easy to slave the cavity length by using the peak due to 
saturated absorption as a reference (fig. 19 (c) and (d)). Since this peak is 
very sharp, the slaving can be extremely precise. 

Since the absorption is due to a nonexcited gas under low pressure, 
the frequency /Ii is subject to only a little perturbation. In addition, we can 
choose a gas whose useful absorption line is to a certain degree insensitive 
to electric and magnetic fields. This is the case for methane at A = 3.39 
^tm. There exist, however, some effects which broaden or displace the ab- 
sorption line: duration of interaction with the waves limited by the transit 
time of the molecules, perturbation of the molecules by the intense elec- 
tromagnetic field of the laser radiation or by nearby molecules, differences 
of saturation for different components when the absorption line exhibits a 
nonresolved structure, Doppler effect of the second order, etc. [18,20]. 
These effects are always small; the corresponding frequency displace- 
ments, which rarely exceed several kilohertz, say a few parts in 10'" for 
relative value, can in large measure be made reproducible. 

Other parasitic phenomena can involve an apparent displacement of 
the peak due to saturated absorption. If this peak is located on the power- 
length characteristic in a region of appreciable slope, its summit is dis- 
placed in relation to the frequency (fig. 20). Similarly, if parasitic electric 
potentials appear in the servomechanism, the length of the cavity may be 
stabilized to a value slightly altered from that which corresponds to the top 
of the peak. 

These last effects are, however, weaker for a narrower peak. In 
this regard, saturated absorption lines provide an essential safeguard 
for metrology. 



"There is an analogous phenomenon, predicted by W. E. Lamb. Jr., which causes the Lamb 
dip in the case of emission (fig. 19 (a)); consequently, the peak due to saturated absorption is 
sometimes called "inverse Lamb Dip." Since emission occurs in a strongly perturbed medi- 
um, the Lamb dip of emission is very broad and less stable than the peak due to saturated ab- 
sorption. 

96 



I 



A P 





Figure 20. Shift of the top when a peak due to saturated alisorption is superposed on the 
characteristic P (I) in a region of appreciable slope. 



Measurement of Frequency Differences by Beats 

Thanks to the very high stability and to the very low spectral width of 
radiations from stabilized lasers, one can display and measure, as in 
acoustics, the beats between the radiations of two lasers having neighbor- 
ing frequencies f and f>. To do this, a single photoelectric sensor is simul- 
taneously illuminated by the beams from the two lasers, beams which are 
superposed with the help of a semi-transparent mirror. The illumination of 
the sensor and the current it delivers are modulated at the beat frequency 
A/=/i — fi. The frequency A/ of the current modulation is measured by 
the customary techniques of electronics. 

This method is limited at high frequencies only by the response of the 
photoelectric sensor to the modulation of the light. It permits precise stu- 
dies of the frequency displacement effects mentioned in the preceding sec- 
tion. It also permits intercomparison of frequencies, hence also of 
wavelengths, of lasers locked to the Lamb dip or to nearby saturated ab- 
sorption lines. In this way, the intervals among a hundred absorption lines 
of iodine, in the neighborhood of 0.633 /u,m, have been measured. These in- 
tervals range from some 10 megahertz to a gigahertz [18]. This method is 
also used in the periodic calibration of lasers locked to the Lamb dip {k ~ 
0.633 ^tm) by using a reference laser locked to the saturated absorption of 
iodine. 

Finally, this is the only present method which permits evaluating the 
stability and reproducibihty of the frequency (thus of the wavelength) of 
radiations from lasers locked to saturated absorption lines of iodine or 
methane. In this way have been measured, over times from several seconds 
to several hours, stabilities better than 10" for iodine and lO^'^for methane, 
with reproducibilites of the order of 10"' and 10" respectively. 



97 



Measurement of Wavelengths 

Wavelengths of helium-neon lasers locked to methane (X ~ 3.39 /itm) 
and to iodine (A = 0.633 (xm) have been determined in several laboratories. 

At the BIPM, we have used the Michelson interferometer for direct 
comparison of these wavelengths with that from the krypton-86 lamp [21]. 
If the interferometer is illuminated with two radiations of respective 
wavelengths A.i and A.o successively, and if the path difference is varied by 
AD, the ratio of the variations of interference order, Api = AD/\i and Ap2 = 
ADjki, gives the ratio of wavelengths immediately. We have systematically 
used path differences D of ±375 mm leading to the maximum precision in 
the case of krypton radiation. 

Figure 21 summarizes the results of these measurements. They have 
supplied the mean values of wavelengths which have been recommended 
by the CIPM [18]. They have also allowed experimental evaluation of the 
uncertainty with which the 1960 definition of the metre can be reahzed; 
this uncertainty does not exceed ±4 X 10 ■'. 

In the case of iodine, several absorption lines can be used for locking. 
Their frequency differences, measured by the beat method, are known 
with a precision largely sufficient for deducing all the wavelengths from 
any one of them. 

The frequency of the laser locked to methane, measured elsewhere 
[22], is /-SB 376 181 627 kHz to within ±50 kHz. This measurement in 
conjunction with those of the wavelength \ of the same laser, supplied the 
value of the speed of light in vacuo which was recommended by the CCDM 
in 1973 [18]: 

c=\/=299 792 458 m/s. 

The major part of the uncertainty comes from the uncertainty in the 
realization of the definition of the metre (±4 X 10"''), leading to an uncer- 
tainty in the value of c of ±1.2 m/s, nearly a hundred times smaller than 
that of the best earlier determinations. 

It can be predicted that the speed of light and lock-stabilized lasers 
will play an important role in length measurements and will perhaps be the 
basis of a new definition of the metre. Studies carried out by the BIPM in 
this field now prepare for this possibility. 



98 



® 



pm 
,420 



NBS(G) 



,410 

3 392 231,400 
,390 
,380 



NRC 



NBS(B) 



BIPM 



-A-^4x10 



-9 



® , 



pm 

404 



A 



NSL 



NBS NRC 



BIPM 



"PTB 



NPL T 

4^- 



4x10 



,402 
632 991,400 
,398 
,396 
,394 
.392 



Fi>;ure 21 . \\ a\ (•leniitlis in picometres (1 pm = lO"'- m) iif lasers locked to abscirption lines of 
nietlianr (al m iiiiline (b). Values measured in various laboratories, with their uncertainties, 
and rcccinimcndcd values. 



99 



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100 



[14] Terrien, J. and Hamon, J., Mesure de la longueur d'onde des radiations etalons secon- 
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Proc. of the Fourth International Conference, Teddington, 1971, J. H. Sanders and A. 
H. Wapstra, Eds., Plenum Press, London and New York, pp. 348-354 (1972). 

[22] Evenson, K. M., Wells, J. S., Petersen, F. R., Danielson, B. L., and Day. C. W., Accurate 
frequencies of molecular transitions used in laser stabilization: the 3.39 fjum transition 
in CH4 and the 9.33 /xm and 10.18 p.m transitions in CO2, Appl. Phys. Letters 22, pp. 
192-195(1973). 



101 



CHAPTER IV 



GRAVIMETRY 



Metrological Importance of the Knowledge 
of the Acceleration of Gravity 

The most precise method of realizing a known force F consists in 
utilizing the action of the terrestrial gravity field on a mass m, known by 
comparison with the standard kilogram. This action, when it exerts itself on 
a body free to move vertically, gives it an acceleration g. The fundamental 
relation of dynamics F=mg permits relating F to the base quantities 
length, mass, and time provided that the value of gis itself determined in 
an absolute manner by means of measurements of length and time. 

For example, the definition of the ampere and consequently of all the 
electric units involves a force and therefore in practice requires the 
knowledge of g. Similarly, the measurement of pressure with the aid of 
liquid manometers requires not only the measurement of the height of a 
column of liquid and the determination of the mass density but also the 
knowledge of g. 

The importance of the knowledge of g, with the maximum precision, 
did not escape the CIPM; as early as 1886, it stated that the anomalies of 
gravity and the irregularities in the form of the Earth required more and 
more serious attention for barometric reductions; it recommended that the 
acceleration of gravity be determined locally, at places where fundamental 
barometric measurements are carried out and particularly at the Pavilion 
de Breteuil. Three methods were utilized successively at the BIPM; the 
first was based on the utilization of reversible pendulums; the second util- 
ized the free fall of a graduated scale; the third, to which further improve- 
ments are still being made, employed the symmetric free motion (ascend- 
ing, then descending) of an optical reflector; it is called the "method of two 
stations." 



Reversible Pendulums 

In 1888, a measurement of the acceleration of gravity was carried out 
at the Pavilion de Breteuil by Defforges of the Geographic Service of the 

103 

573-106 O - 75 - 8 



French Army, following a request from the CIPM [1]. The use of reversi- 
ble pendulums of symmetric exterior form and having interchangeable 
knife edges permitted elimination of the influence of air resistance and of 
the imperfection of the knife edges. The use of pendulums of different 
lengths but of the same mass, and oscillating on the same knife edges, 
eliminated the combined effects of the support motion and the sliding of 
the knives as well as certain systematic errors in the determination of the 
knife edge separations of the two pendulums. The uncertainty of the result 
obtained (^=9.809 91 m/s-) seemed to be less than 5 X 10"'' m/s-, or 5 units 
in the last place. 

The absolute measurement carried out at Potsdam in 1905 by F. 
Kiihnen and Ph. Furtwangler [2], also based on the use of reversible pen- 
dulums, served as the point of departure for the "Gravimetric system of 
Potsdam." From the value of obtained at this location, the values of gat 
various points on the Earth have been deduced by use of connections, that 
is to say by measurements of differences, effected by means of relative 
gravimeters of either pendulum or spring type. In this system, the value of 
g at the Pavilion de Breteuil (point A) is 9.809 398 m/s-. Note that the value 
of Defforges differs from this by 5 X 10^ m/s-. 

The exactness of these measurements, however remarkable for the 
time, was put in doubt and several new determinations were carried out by 
similar methods between 1920 and 1940; the best known are those by P. R. 
Heyl and G. S. Cook in the United States and by J. S. Clark in Great 
Britain. It appeared that the Potsdam system was blemished by an error of 
10 to 20 X 10 m/s-'. The difficulties of methods based on the use of pendu- 
lums seem to consist of the exact evaluations of certain corrections [3], 
notably those which are due to the elastic distortion of the oscillating pen- 
dulums. It was desirable to conceive an entirely different method. 

Free Fall of a Graduated Scale 

In 1946, timed motion pictures of a graduated scale in free fall in vacuo 
was proposed [4]. The law of motion, that is to say the expression for the 
vertical distance h of the center of gravity of the scale from a horizontal 
reference plane, as a function of the time t counted from an arbitrary 
origin, is h = hi) + vot+ 1/2 gt'^, assuming constant throughout the trajecto- 
ry of the scale. It is seen that knowledge of the position of the scale for 
three values of fis theoretically sufficient for the computation of g. One can 
therefore be content with three images; actually, one uses many more in 
order to increase the precision. A preHminary determination by this 
method was made; it was finished in 1951. It appears that the result ob- 
tained (9.809 16 m/s^) suffered from several systematic errors, due mainly 
to friction of the residual air. 



104 



The studies were continued with the aim of improving the accuracy of 
the measurements. These researches were completed in 1958 with a new 
determination [5]. Let us give some details of this work. 

The body which undergoes free fall (fig. 1) is a 1 -metre scale of 
platinum-iridium bearing millimetre divisions over its whole length. The 
scale is furnished with ferrules used on the one hand to keep it vertical 
between two supports, and on the other hand, after the fall, initiated by 
removal of the lower support, to catch the scale by a device giving gradual 
braking. The mean temperature of the scale, also the temperature gradient, 
is determined by the use of two thermocouples attached to the support. 

The fall is carried out in a cylindrical enclosure within which is a 
vacuum of the order of 0.007 Pa. A photoelectric device permits verifying 
that the scale remains vertical during its fall. 

The graduation of the scale is photographed at regular intervals during 
the fall. For that purpose, an optical system forms, on a film placed on a 
rotating drum, the superposed images of the marked surface of the scale 
and of a fixed reference mark. 

Illumination is provided by a spark gap controlled by a quartz oscilla- 
tor; it produces flashes at regular intervals, adjusted as appropriate to the 
experiments, say at the values 10 ms or at 8 ms. 

The initiation of the fall and the start of the train of flashes are con- 
trolled by the rotation of the drum itself. Thus, for each fall, about 50 
images are available on the film. After development, the exact positions of 




Figure 1. Measurement of ^ by method of fall of a jiraduated scale (a) Diajiram of the optics. 
The firaduation of the scale R is illuminated by sparks in the {lap S. through the objectives 
G and A and the semi-transparent plate H. The objectives A and B form an image of this 
graduation on the glass plate C carrying a reference mark. The objective D gives, on the 
film placed on the drum E. an image where the graduation and reference marks are super- 
posed, (b) Appearance of an image of the marks of the scale and the reference. 



105 



the scale are obtained by locating each image of the graduation of the scale 
and the fixed reference mark by means of a micrometer microscope. Cor- 
rections are applied to the positions found, to take account of the calibra- 
tion of the subdivisions of the scale. Computation of the acceleration is 
made by the method of least squares making equal use of all the images. 
The value obtained is corrected for the exact length of the scale consider- 
ing its temperature, also for the departure of the exact frequency of the 
quartz oscillator, determined by comparison with a standard frequency 
transmission, from its nominal frequency. 

The value of g cannot be considered as constant throughout the height 
of the fall, but we can assume that it varies linearly as a function of eleva- 
tion, its increase being about 3 X 10" m/s- when the elevation diminishes 
by 1 m. It is established that the calculation method used gives the value of 
g at a point situated at the distance 2At/7 below the location of the center 
of gravity before the drop, /?t being the total height of fall. The result ob- 
tained is transferred to reference point A of the BIPM gravimetric station 
by means of an experimental value of the gradient oi g. 

Finally, the attraction of the Sun and Moon produce a variation of g, 
called gravitational tide, whose maximum amplitude is 1.6 X lO"*^ m/s-. Ta- 
bles resulting from a theoretical evaluation permit calculating the small 
correction which results from this effect. 

Finally, the value found at the Pavilion de Breteuil (point A) is g= 
9.809 280 m/s-. We note that the value of g at this point on the Potsdam 
system differs from this by 11.8 X 10 m/s-. 

Method of Two Stations 

This method, advocated as early as 1947 [6], was put into operation at 
the BIPM beginning in 1960 [7]. The first results were obtained in 1966. 
Their relative precision was then estimated at 1 X lO"'^. Improvements of 
the apparatus since that date have allowed reaching the present precision 
(early 1974) of 3 X 10~". To get a feel for this precision, one can note that g 
varies by 3 X 10"" (in relative value) when the altitude of the point of mea- 
surement changes by 1 cm. 

Principle 

A body projected vertically upward in vacuo crosses two horizontal 
planes. Si and S2 (the "stations"), whose separation h is known (fig. 2); if t\ 
is the time between the two passages of the center of gravity of the body at 
the lower station in the course of its ascent and descent, and t> the 
analogous quantity for the upper station, it is easily established that g'ls 
given by the relation S/i/fii'- — t-r). 



106 



h 




Figure 2. Principle oi the iiieusiirenieiit of g by the inethiid <il two ^lalidns. The curve 
(parabola) represents, as a function of time /. the height ; reached by the center of gravity of 
an object launched vertically upward. If Ix and ti are the intervals which separate the 
ascending and descending passages of the point past the stations Si and of separation lu 
the acceleration ol the object is 



In fact, by virtue of the vertical gradient of g which is supposed con- 
stant along the trajectory, this formula gives the exact value of ^ at a point 
situated at the distance hl6 + h'l3 below the summit of the trajectory, h' 
being the distance between the upper station and the summit. 

This method presents the advantage of automatically eliminating the 
systematic errors due to the possible braking forces due either to residual 
air or to eddy currents caused by the inhomogeneity of the Earth's mag- 
netic field, since these forces change sign with the reversal of velocity of 
the body: they add to its weight during the ascent and subtract from the 
weight during the descent. Furthermore, this facilitates the time measure- 
ment since at the beginning and end of each of the intervals and t> the 
body passes the same position with the same velocity (apart from sign). 

However, if high precision is sought, putting this method into opera- 
tion presents serious metrological and technical difficulties. The relative 
precision of 3 X 10 •' for g requires the following precisions: 1 nm for h of 
the order of 400 mm, 0.3 ns for ti of about 0.6 s and 1 ns for ti in the 
neighborhood of 0.2 s. The body must be launched upward by a motion of 
vertical translation with extremely severe tolerances as to its direction (3 X 
10"^ rad) and as to its motion in rotation (1 X 10"- rad/s). Furthermore, it is 
necessary to use a reference base stable to a few nanometres, protected 
from ground vibrations and shocks due to the launching. 



107 



Implementation 



The essential part of the absolute gravimeter (fig. 3) is a fool-proof 
Michelson interferometer [8]. An optical corner reflector is used as the 
projectile. The two stations are virtual horizontal planes. When the apex of 
the corner reflector crosses one or the other of these planes, the end mirror 
of the vertical arm of the interferometer is conjugated with one or the other 
of the two mirrors placed in the horizontal arm. 



Fb 




Figure 3. Diagram of the absolute gravimeter of the BIPM. The apparatus comprises two 
evacuated compartments connected by flexible bellows S. The vertical compartment CI 
(residual pressure 2 X 10"'' Pa), provided with a magnetic shield B, is the place for the 
ascending then descending, free fall of the mobile corner reflector Tm. This is shown at the 
lower station (full lines) and at the u|iper station (dotted) at the distance h. 

The horizontal compartment C2 (residual pressure 1 x 10"- Pa) contains the fixed por- 
tions of the measuring interferometer: beam s|)litter L, fixed corner reflect<ir Tf, etalon E, 
of length 'Ih ~ 0.8 m. This interferometer, illuminated by the beam of white light Fb (full 
lines) gives, when the mobile reflector passes the lower and upper stations, an interference 
phenomenon I (achromatic fringe). 

This compartment is placed on a platform T whose stabilization is assured by a wire 
suspension F, an oil damper H, and the piezoelectric elements P. These last are controlled 
by the accelerometer A and by the signals from a seismometer of very long period support- 
ing the corner reflector Tr whose apex constitutes a reference point w ilhout appreciable ac- 
celeration. The residual vibrations of C2 with respect to Tr are recorded at V with the aid of 
an auxiliary interferometer illuminated by the monochromatic light beam Fm (dashed 
lines); one takes account of these vibraticuis in correcting the value of ^obtained. 



108 



For these positions, the path difference in the interferometer vanishes 
and interference fringes can be produced with white light. They are de- 
tected by a photomuItipHer. The central fringe, or achromatic fringe, is 
used for starting and stopping the timing counters. By reason of the small 
width of the beams used and the high frequency of the signal given by the 
photomultiplier, an ordinary source of white light is not suitable for giving 
a good signal/noise ratio; one must use a xenon lamp whose flashes are trig- 
gered at each station passage, at ascent and descent, by means of an ap- 
propriate predetection device. 

Measurement of Distance 

The length 2h of the etalon constituted by the two fixed mirrors of the 
horizontal arm of the interferometer is determined by direct comparison 
with the primary standard radiation of krypton-86 using the same inter- 
ferometer as for the measurement of g. For this measurement, the movable 
corner reflector is fixed halfway between the two stations. Although the 
visibility of the interferences thus obtained is weak (5%), the precision of 
1 X 10"-' can be assured. Use of the radiation from a helium-neon laser 
locked to a saturated absorption line of iodine, whose wavelength is stable 
to about 1 X 10 and for which a value has recently been recommended 
(CCDM, 5th session, 1973), greatly facilitates this measurement and cur- 
rently permits attaining a precision of 0.7 X 10 

Projectile and Catapult 

The projectile (fig. 4) consists of six plane mirrors forming two corner 
reflectors back-to-back at the apex and mounted on a frame of aluminum 
alloy. Only one corner reflector is used, but this symmetric construction 
facilitates placing the common apex of the two reflectors in coincidence 
with the center of gravity of the assembly. The frame is pierced with the 
openings needed for the passage of the light beam. An axial bore gives 
passage for the elastic cord which serves for launching. The projectile is 
accelerated over a distance of 0.30 m and then follows freely its movement 
after blocking of the catapuh. After a travel of 0.18 m, of 0.05 s duration, in 
the course of which its internal oscillations die out, it traverses the lower 
station and then, after 0.2 s, the upper station. The peak of the trajectory 
normally occurs 50 mm above the upper station. In the descent, after a new 
traversal of the upper and lower stations defining the intervals ti and to. the 
projectile is braked by elongation of the elastic cord of the catapult. 

This cord, in the course of its contraction, develops electric charges. 
Their effect on the projectile is eliminated by a metallic tube surrounding 
the cord and forming an electrostatic screen. 



109 




0123456789 10 

cm 

Figure 4. Projectile (mass 430 g) for the measurement iif g by the two-station method. There 
are shown the six plane mirrors forminfi two corner reflectors back-to-back at the apex, the 
openings for tlie passage of light, and tlic central bore for the passage of the elastic cord of 
the catapult. 




Stabilized Platform 

The horizontal compartment containing the essential parts of the 
Michelson interferometer rests on a platform which is protected from 
vibrations and ground movements by means of various devices. 

Suspension by wires and viscous dampers eliminates horizontal vibra- 
tions at frequencies above 5 Hz. A set of piezoelectric bearings and a verti- 
cal accelerometer of short period constitute a counteracting system which 
attenuates rapid vertical movements of the ground (5 to 50 Hz). These 
bearings also carry elements controlled by a vertical seismometer of very 
low natural frequency and elements permitting the fine adjustment of the 
horizontality of the platform. 

The residual accelerations of the reference system are currently less 
than about 10"*' m/s-. say 10"-' g. 

Measurement of Time 

The intervals t\ and t-z are measured in two steps. A resolution of 50 ns 
is obtained by means of counters at 20 MHz; then a resolution of 0.1 ns is 
obtained by interpolation on a photographic recording of the white light in- 
terference fringes; this recording carries time reference marks at a 
frequency of 20 MHz. In practice, the chronometers are preset to measure 
successively three intervals; t^, the duration of the ascent from the lower 
station to the upper station, to already defined, and t^\, the duration of the 
descent from the upper station to the lower station. Thanks to the sym- 
metry of the motion, ascending then descending, the effect of the air re- 
sistance is negligible at pressures p < 1 Pa with the condition that this 
residual pressure remain constant during the whole displacement. At 
present, we work with residual pressures of the order of 2 X 10"^ Pa. The 
difference ^^t — t^\ — t^ then varies linearly as a function of p. If one ex- 
trapolates to zero pressure one finds A?=+5.3 ns, a result conforming per- 
fectly to that foreseen in the case of no braking, taking account of the finite 
value of the speed of light. This confirms the exactness of the time mea- 
surements. 



Recording of the Gravitational Tide 

We have seen that the perturbation of due to the luni-solar effect has 
for its maximum value 1.6 X 10"" m/s-; its rate of variation can reach ±0.8 
X 10"* m/s- per minute at the BIPM station. It is necessary to know this 
perturbation with an uncertainty at most equal to 0.5 percent of its am- 
plitude and at times known to about a minute, or better, to make the mea- 
surements of ^ from day to day consistent with each other. 



Ill 



The precision of the theoretical determination of the gravitational tide 
running the risk of being revealed insufficient, a recording station 
equipped with a relative gravimeter has recently been installed (October 
1973) at the BIPM. The protection against microseisms and the stabiliza- 
tion of the pressure and temperature have been specially studied, and we 
can confirm the values of the gravitational tide found with the absolute ap- 
paratus. The drift of the relative gravimeter is currently less than 1 X lO"'^ 
m/s- per month, which is 30 times less than for the best commercial ap- 
paratus. The combination of absolute and relative apparatus is favorable to 
both: the true correction for gravitational tide is now available for the ab- 
solute apparatus and this latter permits the calibration of the relative 
gravimeter and the determination of its long-term drift. 

Results and Studies Underway 

The results obtained since 1966, transferred to the reference point of 
the gravity station of the Pavilion de Breteuil (point A), thanks to a positive 
relation by means of relative gravimeters, has the mean value 9.809 260 
mis'. 

It is seen that the value found in 1958 differs from this by 2.0 X 10~^ 
m/s- and that the value in the Potsdam system differs from it by 13.8 X 10"^ 
m/s2. 

This result, joined with those of other laboratories, has led the CIPM 
to add to the Potsdam gravity system a correction of — 14 X 10 m/s- 
(Resolution 1 (1968)). 

By reason of the precision attained, this corrected system was soon 
surpassed. In 1971, the International Union of Geodesy and Geophysics 
created a "Unified International Gravity Net" (IGSN-71) by adjustment of 
a large number of absolute and relative measurements of precision at least 
as good as 10"' carried out at various points of the globe. The CIPM 
adopted this net (Recommendation 2 (CI-1972)) and its future updatings for 
metrological needs. The BIPM station (point A) is the point where the mea- 
surements are the most precise and the systematic errors the most 
completely studied. It has been chosen as the starting point of this net and 
as the verification point for transportable absolute measurement ap- 
paratus. 

Since 1968, the BIPM has given its help to the Istituto di Metrologia 
G. Colonnetti (Turin) in the construction of a portable absolute gravimeter 
[9]. The principle of this gravimeter is identical to that of the stationary ap- 
paratus of the BIPM (fig. 5) except with regard to the determination of the 
separation of the two stations which is carried out by the use of reversible 
counting of interference fringes of a stabiHzed and calibrated helium-neon 
laser. On the other hand, the optical reference corner reflector is supported 
by a vertical seismometer of long period; this avoids registering 

112 



I • I 




Ascent 



Summit 



Descent 




Figure 5. Transportable absolute gravimeter. (a) Diagram of principle. Tm. mobile corner 
reflector; Tf "fixed" corner reflector supported by a long-period vertical seismometer; L, 
helium-neon laser emitting a monochromatic radiation of wavelength \; S, beam splitter; 
two photomultipliers P and P' are used to furnish sinusoidal signals out of phase by approx- 
imately one quarter period, which permits reversible counting. The apparatus is supported 
by piezoelectric bearings C, elements of an antivibration mounting, (b) Signal from one of 
the photomultipliers as a function of time t. The upper station is defined by the last fringe 
counted on the ascent and the first fringe counted on the descent. The lower station is 
defined in the ascent by the start of the counter at a predetermined instant and in the 
descent by its return to 0: n fringes being counted in the ascent (and deducted in the 
descent), the distance between the stations is h = n \/2. The intervals and N are measured 
by counting pulses at a 50 MHz rate. 



113 



microseisms and determining the corrections due to them. Finally, the ap- 
paratus operates with a modest vacuum (1 Pa), which is sufficient to insure 
an accuracy better than 5 X 10 m/s'; this has permitted simplification of 
the pumping system. This apparatus, recently tested at the Pavilion de 
Breteuil, gave for each series of 25 measurements a mean result agreeing 
with the accepted value to better than 2 X 10"^ m/s-. It will permit the early 
reahzation of numerous gravimetric links, even over large distances, 
without risk of drift. In particular, the difference of the values of g between 
the stations at Sevres and at Turin (about 0.003 9 m/s-), will become the 
most precise base for the calibration of relative gravimeters, and its exact 
knowledge will contribute greatly to the precision of the Unified Interna- 
tional Gravity Net. 

But naturally, measurements made with a fixed apparatus can be more 
precise than the data of this Net. This is indeed the case for the measure- 
ments made at the BIPM. They show up effects which up until now had not 
been capable of being demonstrated. 

Figure 6 gives some of the values of g obtained since 1966. 

It is seen that g is subject to variations reaching 40 X 10^*^ m/s'; their 
origin is unknown. Some years of study will still be needed to clarify this 
point which could have important metrological, geophysical, and as- 
tronomical consequences. 



9,809 2600 



9,8092595 




1 1967 


1968 


1969 


1 1970 


1971 


1 '^^^ 


1973 1 


1 r 1 1 1 1 1 1 1 1 1 J 1 1 


1 1 < J 1 1 


1 I 1 1 I 1 i 1 1 1 [ 


1 1 


1 M 1 1 1 1 1 1 1 


1 1 1 1 1 1 1 1 


1 1 1 1 1 1 1 1 1 1 1 1 y 



Fiiiure 6. Monthly means of tlie values of obtained at the measuring point and transferred to 
jioint A. reference ]ioint ol llic BIl'M gravity station. Eaeli of these means carries some 50 
measurements. Tlie error Ijars represent the uncertainty of a measurement, calculated 
from the dispersion of individual results. The transfer from the measuring point to the point 
A introduces a supplementary uncertainlv roimnori to all these values and assessed at 3 X 
10 " m/s-. 



114 



Bibliography 



[1] Defforges, Mesure de Tintensite absolue de la pesanteur, Proces-Verbaux C.I. P.M.. pp. 
135 182 (1891). 

[2] Kiihnen, F. and Furtwaiifiler, Ph., Bestimmung der absoluten Griisse der Schwerkraft 

zu Potsdam mit Reversions pendeln, Veroff. Kdnigl. Preuszischen Geod. Inst., No. 27. 

xvi + 390 pages, Berlin (1906). 
[3] Cook, A. H., The absolute determination of the acceleration due to gravity. Metrologia 

1. No. 3, pp. 84-114(1965). 
[4] Volet, Ch., Sur la mesure absolue de la gravite, C.R. Acad. Sc. 222, pp. 373-375 (1946). 

Volet, Ch.. Mesure de I'acceleration due a la pesanteur au Pavilion dc Breteuil. C.R. 

Acad. Sc. 235, pp. 442-444 (1952). 
[5] Thulin, A., Determination absolue de racceleration due a la pesanteur au Pavilion de 

Breteuil, Travaux et Memoires du B.I.P.M. 22 (1),91 pages (1961). 
[6] Volet, Ch., L'intensite de la pesanteur determinee par la chute d'un corps. C.R. Acad. 

Sc. 224, pp. 1815-1816(1947). 
[7] Sakuma, A., Recent developments in the absolute measure of gravitational acceleration, 

Nat. Bur. Stand. (U.S.), Spec. Publ. 343, pp. 447-456 (August 1971), and Recueil de 

Travaux du B.I.P.M. 3, article 15 (1971-1972). 

Sakuma, A., A permanent station for the absolute determination of gravity approach- 
ing one microgal accuracy, Proc. Symposium on Earth's gravitational field and secular 
variations in position. University of N.S.W., Sydney, pp. 674-684 (1973), and Recueil 
de Travaux du B.I.P.M. 4, article 11 (1973-1974). 
[8] Proces-Verbaux C.I.P.M.. p. 49 (1960). 

[9] Cerutti, G., Cannizzo, L., Sakuma, A., and Hostache, J., A transportable apparatus for 
absolute gravity measurement, VDI-Berichte 212, pp. 49-51 (1974), and Recueil de 
Travaux duB.I.P.M. 4, article 12 (1973-1974). 



115 



CHAPTER V 



MANOBAROMETRY 



From the beginning of the BIPM. the responsible scientific leaders 
recognized the necessity of an apparatus which permits the precise evalua- 
tion of the atmospheric pressure (barometer) or, more generally, of other 
pressures (manometer) and, less than 10 years after its creation, the BIPM 
constructed a quality manobarometer (fig. 1); this apparatus competed suc- 
cessfully, practically without essential modification, with the various 
developments which appeared successively in the world in the course of 
the first half of the 20th century. It was a mercury apparatus with several 
original features, the first manometer, for example, to have large diameter 
menisci (about 37 mm) rendering negligible the influence of capillary defor- 
mation. The vertical distance between the central parts of the two menisci 
was determined optically, by transfer to a vertical calibrated scale with the 
aid of the two horizontal telescopes of a cathetometer (fig. 2); to define the 
surface of a meniscus, the optical procedure adopted as early as 1890, al- 
ready very much elaborated, utilized the middle point between a reference 
(glass point placed inside the chambers of the manometer) and its image 
reflected by the mercury. Furthermore, the apparatus had been filled with 
mercury by distillation under vacuum [1 ]. 

It is rather difficult to estimate with what accuracy one can determine 
a pressure with this apparatus. The pressure p is deduced from the relation 
p — hpg, where h is the level difference between the two mercury menisci, 
p the mass density of the mercury, and g^the acceleration of gravity. Even 
aside from the optical and mechanical errors which affect the measure- 
ment of the length h and which prevent a precision better than 10 fxm (or 
about 10"'^ of the atmospheric pressure), the two other factors p and gwere 
not known to better than about 10^^. and this was so at least until around 
1930. 

In practice, it was necessary to await the years after 1950 for profound 
metrological studies based on the rapid progress of technology to improve, 
almost simultaneously, the knowledge of p and g; p is now known to about 
10"'' [2] and gto better than 10"' [3]. We could therefore envisage improv- 
ing the measurement of pressure, conditioned, however, on conceiving a 
new manobarometer in which the determination of the height of the mercu- 



]17 



ry would be possible to about 1 in 10'*. The study of a new apparatus was 
therefore undertaken, because the reaUzation of a more precise tempera- 
ture scale, based on fixed points corresponding to the boiling temperatures 
of pure substances, demanded a knowledge of pressure to a few parts in 
10**. And even today when the progressive abandonment of boiling points 
renders the problem less crucial in thermometry, the precise measurement 
of pressure becomes necessary in other areas, for example in the com- 
parison of mass in all the cases where air pressure plays a role. 




118 




Figure 2. Diagram of the standard manobaroineter of 1884. C. cathetometer; R. graduated 
scale: Mi, M2, chambers of the manometer; Bi. B.. chambers of the barometer; RM, mercu- 
ry reservoir (the four chambers and the scale are at the same distance from the cathetome- 
ter). 



Interferometric Manobarometer 

The apparatus studied at the BIPM and put into service in 1966 [4] is 
still a mercury manobarometer. Mercury is still the most suitable liquid: it 
can be obtained very pure, its thermal conductivity (that of a metal) is good, 
and its mass density is high. The originality of this apparatus resides in the 
device for localizing the mercury surfaces, which allows substituting for 
the measurement of a not directly accessible vertical distance, the easy 
measurement of a horizontal displacement (fig. 3). 

This device utilizes the interference of light, not for measuring the 
distance which separates the two mercury menisci, but simply as an optical 
feeler; for this, one depends on the behavior of white light interference 
fringes which appear when the two optical paths are sensibly equal (to 
about 1 jJLm). The two mercury surfaces are used as mirrors in a Michelson 
interferometer; the optical path difference which appears when there is a 



573-106 O - 75 - 9 



119 




Figure 3. Dia<zium of the standard mannbarometer placed in service at the BIPM in 1966. A. 
reference mirror; B. source of white light; C. photomuitiplier; D. oscilloscope; E. graduated 
scale; F, suspension spring: C annular oil damper: H. measurement chamber; I. aluminum 
envelopes; J. thermal insulation; K. reservoir chamber; L, supporting frame; M, carriage: 
N. optical corner reflector; O. optical reflecting prism; P. oscillating compensator plate; Q. 
beam splitter. 

The measurement ol a |iressure comprises two operations. First, one evacuates the two 
measurement chambers and disjilaces the carriage bearing the two corner reflectors and 
the scale to the point of obtaining fringes on the oscilloscope screen; a reading of the scale 
by means of a microscope |>rovide(l with a micrometer then furnishes the ""zero" of the ap- 
paratus. One of the chambers is then put in communication with the closed space in which 
one wishes to know' the pressure and. by a procedure analogous to the preceding, a second 
reading on the scale is obtained. The difference of the two readings gives, after various cor- 
rections, the level difference between the two mer cury menisci. 



120 



Figure 4. Image observed on the osc illoscope screen. When one observes a packet of several 
fringes, approximately centered on the oscilloscope screen, tiie adjustment is reached (the 
length of the packet corresponds to a carriage displacement of less than 1 fj.m}. 



change in the relative positions of the two menisci, that is to say, when the 
pressure is changed, can be compensated by the displacement of two solid 
optical elements; this displacement, measured on a calibrated scale, in- 
dicates the change of height of the mercury. The interference fringes are 
observed on the screen of an oscilloscope (fig. 4) whose sweep is 
synchronized with the oscillatory movement of the compensation plate of 
the interferometer; this movement creates the small variation of path dif- 
ference needed for exploration of the fringes. 

Some corrections are, however, necessary. For example, the use of 
light interference involves the indices of refraction of the different media 
traversed by the light; now the ambient air and the nitrogen contained in 
the measuring chamber have slightly different indices of refraction and are 
not equally dispersive; it results from this that, in general, equality of the 
optical paths does not rigorously correspond to equality of the geometrical 
paths (fig. 5). The correction term, a function of the pressure to be mea- 
sured, and easily calculated, never exceeds 5 Pa, however. The 
manobarometer thus permits measuring pressure in the entire range from 
0 to a little above 10^ Pa, with an accuracy of 0.1 to 0.2 Pa. that is to say, to 
about 1 in 10*^ in the neighborhood of atmospheric pressure. 



Source of 
white 
light 



Source of 

white 
light 





Sensor 



vacuum 



Nitrogen 



If 



B 



Fifiure 5. Paths of the lifiht beams in the iiiteiferdiiieter. A: for a zero pressure: B: for an ar- 
bitrary pressure, p. Note that the perfect symmetry of the optical paths in the first case no 
longer exists in the second (in fact, one compensates the difference by a difference of 
pathleiigths in air). 



122 



The practical realization of the apparatus has naturally required great 
precautions. In order to utilize the mercury menisci as mirrors, it is neces- 
sary to protect the manometer chambers from vibrations; these exhibit 
themselves by ripples on the mercury surface which weaken the contrast 
of the interference fringes; observations then become difficult without, 
however, any risk of systematic error. We have sufficiently attenuated the 
perturbing vibrations at frequencies above a few hertz by using a damped 
elastic suspension of very low resonance frequency (helical springs and oil 
dampers) and by connecting the manometer chambers to the fixed pipes 
with flexible links. 

For the mercury to retain its initial properties, it is necessary to pro- 
tect against all contamination and, in particular, to avoid exposing it to con- 
tact with the humidity of the air; the manometer chambers are kept under 
an artificial atmosphere of dry nitrogen. Up until now, the manobarometer 
has been used only for comparative measurements, tied to a closed space 
containing dry nitrogen, but nothing would prevent interposing a mem- 
brane for particular applications (gas thermometry, for example). 

Another very important problem concerns the mercury temperature 
which should be very uniform and known to better than about 0.01 K, if one 
wishes to know the density of the mercury to better than 10^"; a double en- 
velope of polished aluminum enclosing a large thickness of a good thermal 
insulating material assures the required uniformity of temperature; an en- 
semble comprising a mercury thermometer and several differential ther- 
mocouples allows determining the temperature at a reference point and the 
temperature differences between this point and the mercury at different 
levels. 

This manobarometer, as it operates at the BIPM, permits either the 
measurement of a pressure or the adjustment of a pressure to a predeter- 
mined value, in a few minutes. 

An apparatus of this type not being transportable, there appears a 
need for pressure transport standards of an equivalent precision; it has al- 
ready been proposed, for example, to use for reference the vapor pressure 
of the triple points of various pure substances. These standards would per- 
mit an interesting comparison of some absolute manobarometers which are 
in service in the large metrology laboratories. 



123 



Bibliography 



[1] Marek, W. J., Pesees executees aii B.I. P.M. du I''' octobre 1881 au 15 Janvier 1883, 
Travaux et Memoires B.I. P.M. 3, (1884), see Instruments auxiliaires, Barometres, pp. 
D22-D51 (1884). 

[2] Cook, A. H., Precise measurements of the density of mercury at 20 °C, Phil. Trans. Roy. 

Soc. 254 A. pp. 12,5-154 (1961). 
[3] Acceleration of gravity: tiiis volume, p. 103,. 

[4] Bonlioure. J. and Terrien, J., The new standard manobarometer of the Bureau Interna- 
tional des Poids et Mesures, Metrologia 4, pp. 59-68 (1968). 

Bonhoure, J., Manobarometre pour la mesure absolue des pressions, Entropie 13, pp. 
57-61 (1967), and Recueil tie Travaux du B.I. P.M. 1 (1966-1967). 



124 



I 



CHAPTER VI 



THERMOMETRY 



The Gas Thermometer and the Mercury Thermometer 

Measurements of length and mass, which were originally the principal 
preoccupation of BIPM, require a good knowledge of the temperature; this 
explains the almost simultaneous development, starting in 1875, of impor- 
tant studies on the gas thermometer and the mercury thermometer [1]. 

The work undertaken utilizing successively hydrogen, nitrogen, and 
carbon dioxide in the thermometer quickly showed that hydrogen was the 
gas closest to the ideal state, and as early as 1887 the CIPM adopted as the 
standard thermometric scale, the centesimal (or centigrade) scale of the 
hydrogen thermometer. This scale was based on two fixed temperature 
points to which were assigned the values 0 and 100: the temperature of 
melting ice and that of the vapor of water boiling under standard at- 
mospheric pressure. 

For practical applications, however, there was needed a measuring in- 
strument which would be more convenient to use than the gas thermome- 
ter. Although in 1875 the reputation of the mercury thermometer was not 
excellent, the BIPM decided to evaluate its possibilities. Techniques were 
developed very rapidly; they consist in determining very carefully all the 
corrections necessary to bring the readings into agreement with those 
which a perfect instrument would give: they permitted reliable and precise 
use of the mercury thermometer. The disappearance, about 1925, of the 
"hard glass" used up until then for the construction of thermometers, al- 
most brought the question up again and almost nullified the value of the 
enormous work which had been accomplished: but the adoption of glasses 
of equivalent quality (Jena glass 16'" for the reservoir, "green glass" for the 
stem) saved the situation. Further progress, which brought the mercury 
thermometer to a high degree of perfection, was marked by two important 
stages. In 1933, the double-graduation stem (front and rear) permitted the 
suppression of parallax error; in the next few years, the feasibility of 
replacing glass by fused quartz made possible the elimination of a limita- 
tion of the mercury thermometer, the instabilities of the zero: "slow climb" 
due to aging of the glass and "depression" due to residual dilatation of the 
glass. It is generally admitted that the mercury thermometer, used under 



125 



the best conditions and by an experienced observer, can give a precision of 
2 or 3 mK. Since 1887, therefore, mercury thermometers which have been 
carefully evaluated and compared to a hydrogen thermometer could pro- 
vide a convenient and precise representation of the standard thermometric 
scale. 

The International Practical Temperature Scale 

Some discussion of the chronological evolution of this practical scale 
of temperature [2] is necessary to estabhsh the orientation of the work of 
BIPM. 

Since the beginning of the century, the need for an international agree- 
ment on a practical temperature scale had been felt; a draft presented by 
the United States of America and soon supported by Germany and Great 
Britain led to the adoption of the "International Temperature Scale of 
1927/' This scale, defined only above — 190 °C, was based on six 
reproducible equilibrium temperatures to which were assigned numerical 
values, and on instruments and interpolation procedures: the platinum re- 
sistance thermometer up to 660 °C, the platinum/ platinum — 10 percent 
rhodium thermocouple up to the freezing point of gold (1063 °C), and the 
Wien radiation law above that. The scale agreed with the thermodynamic 
scale as well as possible and as far as the knowledge of the time permitted 
its verification. 

Some modifications were made to the scale in 1948, in 1960, and in 
1968 to arrive at the scale which is currently in force under the name "In- 
ternational Practical Temperature Scale of 1968"; these had been primari- 
ly for the purpose of extending the scale to low temperatures (down to 13 
K), of replacing the melting point of ice by the more reproducible triple 
point of water and of substituting Planck's ' law for that of Wien. Moreover, 
account had been taken of the increase in the accuracy of measurements, 
and the international practical scale was adjusted so that it gives, within 
the limits of this accuracy, an approximation as close as possible to the 
thermodynamic temperature (fig. 1). 

Note moreover that there is no longer a thermodynamic scale, since 
the kelvin (K), which is the unit of thermodynamic temperature (T), is 
defined as being the fraction 1/273.16 of the thermodynamic temperature 
of the triple point of water (1954, 10th CGPM). Concurrently, there exists 



' Planck's law gives the spectral density of the energy exitance M of a blackbody as a function 
of the wavelength X and the temperature T: 

M = Cik^^{e\p{C2lKT) — 1} Ci and C2 are two constants. 

Wien's law is obtained by neglecting 1 compared to the exponential. The exitance is the quo- 
tient of the flux leaving a surface element of the blackbody, by the area of that element. 



126 



Fixed points (K) 



Instruments 



Interpolation formulas 



TP Hj (eq.) 13.81 

BP (eq.) 17.042 

BP (eq.) 20.28 

TP Ne 27.102 

TP O2 54.361 

BP O2 90.188 

273.15 

TP H,0 273.16 

BP H^O 373.15 

FP Sn 505.1181 

FP Zn 692.73 

903.89 

FP Ag 1235.08 

FP Au 1337.58 



(Scale not defined below 13.81 K) 





® 

Temperature-resistance 




Relation: 




® reference function 




+ difference function 


PLATINUM 


© A, B, C, or D 


RESISTANCE 




THERMOMETER 


Temperatureresistance 
Reiation: 
2 polynomials 


THERMOCOUPLE 
Pt/Pt-Rh 10% 


Temperature-EMF Reiation: 
Second-degree equation 


PYROMETER 


Planclf's Law 
(reference: FP Au; 
C2= 0.014 388 m K) 



Figure 1. FriiK-ipal elements defining the International Practical Temperature Scale of 1968 
(IPTS-68). TP. triple point: FP, freezing point: BP. boiling point under a pressure of 101 325 
Pa: BP*, boiling point uder a pressure of 33 360.6 Pa: eq.. signifies that the hydrogen has its 
ortho-para composition in equilibrium at the temperature considered. 

The instruments should be standardized at the fixed temperature points; at intermediate 
temperatures, the interpolation formidas relate the temperature to the instrument indica- 
tion. 



a Celsius temperature (t), obtained by shifting the zero and defined hy t = 
T — 273.15 K, whose unit is the degree Celsius (°C) which is equal to the 
kelvin. It follows that the temperature of the triple point of water is also 
0.01 °C,by definition. 

The mercury thermometer has never figured as an interpolation in- 
strument in the International Scale, even in the range of ambient tempera- 
tures; the platinum resistance thermometer has always been preferred 
because it is more precise, and also because the same instrument can 
cover a very large temperature range. Since 1897, the BIPM has been in- 
terested in this latter type of thermometer and has studied its properties up 
to 600 °C by direct comparison with a gas thermometer; it verified the re- 
sistance-temperature relation proposed by Callendar and Griffiths. In- 
cidentally, in the course of this work, the BIPM even assigned a value to 
the boiling point of sulfur, a fixed point which was used much later, from 
1927 to 1960, as a reference in the International Scale. But later and for 



127 



various reasons, the activity of BIPM in this area dechned and, as paradox- 
ical as it may appear, it was necessary to wait until 1960 for the beginning 
of the installation at BIPM of the necessary equipment for the realization 
of the International Scale. Today, this installation operates from 0 °C to 
1064 °C with its greatest precision, and it is in operation below 0 °C, both to 
satisfy BIPM's own needs and to respond to calibration requests from na- 
tional laboratories. 



Measurement Equipment of the BIPM 

The installation includes not only the defined fixed points and the 
specified interpolation instruments, but also measuring apparatus. 

The fixed points actually realized are the triple point of water (0.01 °C) 
and the freezing points of tin (231.968 1 °C). of zinc (419.58 °C), of silver 
(961.93 °C), and of gold (1064.43 °C); the boiling point of water, less precise, 
has been abandoned. 

The technique for use of a water triple-point cell (fig. 2) is now well 
established. An ice mantle of well-regulated thickness is obtained around 
the thermometer well by introducing a very closely fitting metallic rod, 
previously chilled in liquid nitrogen; fewer than 10 such operations suf- 
fices, which requires only a very short time, but it is necessary to wait 
several hours if one wishes the thermal equilibrium of the triple point to be 
attained to better than 0.000 1 K. This equilibrium can be preserved for 



PYREX 



WATER Ivaporl 



WATER IliquidI 




WATER IsolidI 



Figure 2. Cell for the triple |i(iint of water. The temperature 0.01 °C is obtained, with water of 
very high purity contaitied in a sealed ampoule, wherever the iee is in ei|uililiriuni with the 
liquid-vapor interfaee. Tlie ampoule should therefore be free of all gas and all foreign sub- 
stanee. 



several weeks if one takes the precaution of placing the cell in a Plexigias 
tube which is itself kept in a tub of crushed ice. 

To reaHze the freezing points (figs. 3 and 4), we have researched the 
techniques which allow the best reproducibihty, for example by blowing 
argon into the thermometer well to initiate crystalhzation in the case of a 
metal which undergoes an appreciable supercoohng (tin). 

Similarly, crucibles are kept in an argon atmosphere to avoid oxidation 
of the graphhe and, in the case of silver, the solution of the oxygen of the air 
into the molten metal. As to ovens, they have a large time constant (greater 
than 10 hours) and muhiple (five) heater windings, which permits obtaining 
a very high stability and a very good uniformity of temperature throughout 
the crucible (0.01 to 0.02 K). 



G 
H 



Figure 3. Diagram of a cavity containing a pure metal, for the realization of a freezing point. 
A, Teflon stoppers; B, guard cavity; C, pure metal; D, argon inlet; E, thermal insulation; F, 
graphite disks; G, thermometer guide; H, graphite lid; I. graphite thermometer well; J, gra- 
phite cavity. 

A step in the curve of temperature as a function of the time corresponds to the solid- 
liquid equihbrium of a very pure metal; one can thus realize very reproducible temperature. 



temperature 




/ / 



Figure 4. Steps of the freezing and melting of a metal. The form of the steps (in particular the 
temperature interval Afj of the fusion step) and the lowering of the temperature of the freez- 
ing step, Afs, give information on the purity of the metal. In the ideal case, Afi, /k-z, At3 
would be zero. 



129 



I 




Figure 5. The Smitli bridge and the measurement of resistance theriiKimeters. The nominal 
values of the bridge resistanceTare: S=1000 fi, « = 10 (1.6 = 990 (1. a, = lOfl: a = (). The 
lead resistances Li. L>, A3, L^ are almost equal (mean value L). 
If the preliminary adjustment of tiie bridge is such that 



a + aJQ + R=blS - R 



one lias, at balance: 



P = {KIS) Q+{L,-L2) + 



b + a,+Q 



One can, by interchange of the leads Li. L^- l^iu with L4, L^. L>- /^i, get rid of the re- 
sistances of the conductors, up to a mean value L which is a function of the precision 
desired for For equivalently for the temperature. In practice, temperature measurements 
are possible to about 10"^ K for L =s2 fl. which allows keeping the Smith bridge at a fixed 
location even for measuring thermometers as far as 100 m away from tiie bridge. 



130 



The interpolation instruments differ on the two sides of 630.74 °C: the 
resistance thermometer below, and the platinum/platinum — 10 percent 
rhodium thermocouple above. The BIPM possesses some resistance ther- 
mometers of recent fabrication: the resistor, of very pure platinum, is en- 
closed in an envelope containing dry air; the thermocouples are completely 
mounted and stabiHzed at the BIPM, starting with wire of suitable charac- 
teristics and purity and with tubes of pure alumina. 

The measuring apparatus comprises a potentiometer of 0.1 resolu- 
tion for the thermocouples, a resistance comparator using alternating cur- 
rent (resolution of few parts in 10") and a type III Smith bridge (resolution 
10 ft, corresponding to 10"^ K for a thermometer having a resistance of 25 
n at 0 °C) for the resistance thermometers. The type III Smith bridge (fig. 
5) is a modified version of the Kelvin double bridge; it is particularly well 
adapted to measuring resistance thermometers because it permits, by in- 
terchange of connections, the almost perfect elimination of the resistance 
of the conductors which connect the thermometer to the bridge; the Smith 
bridge nevertheless requires upkeep and frequent and tedious cahbration. 
This is why a direct current bridge using the principle of the current com- 
parator could advantageously replace the Sinith bridge in the near future. 

The precision of temperature measurement with the resistance ther- 
mometer can be considered as satisfactory: it is better than 0.001 K in the 
range 0-100 °C, for example; at elevated temperatures, it is limited to 0.1 or 
0.2 K by the instabilities of the thermocouple. Studies underway, with the 
aim of reducing this defect, could lead to the abandonment of the ther- 
mocouple as an interpolation instrument; the range of temperature left 
open would be shared between the resistance thermometer which, well 
constructed, can go beyond 630 °C, and the photoelectric pyrometer which, 
with modern detectors, becomes practical below 1064 °C. 

Pyrometric Study of the Freezing-Point 
Temperature of Gold 

There is another problem to be considered, that of the accuracy of the 
values assigned to the defined fixed points: for example, a recent deter- 
mination of the temperature of the boiling point of water by use of the gas 
thermometer seems to show that the uncertainty which affects the tem- 
peratures is perhaps greater than was estimated in 1968, even for tempera- 
tures which were believed to be well known. This is why some work is 
being pursued in laboratories by diverse methods, notably gas ther- 
mometry and pyrometry; the BIPM is participating in these researches and 
has chosen to study the temperature of the freezing point of gold [3]. 

The value assigned to this fixed point in the IPTS-68 resulted from 
several determinations, all made with gas thermometers, whose dispersion 
is greater than 0.5 K; on the other hand, two studies made later by 
monochromatic pyrometry furnish values which are lower by several tenths 



131 



of a kelvin. In the face of these disagreements, the BIPM has undertaken 
a determination, also by a pyrometric method, but under different condi- 
tions of reaHzation. 

The principle of the measurement consists in comparing the 
monochromatic luminances (wavelength in the neighborhood of 1 /u,m) of 
two identical radiating cavities, approximating blackbodies, which are ob- 
served alternately (fig. 6); the cavities are maintained at 630 °C and 1064 °C 
respectively; their temperatures are measured by two thermocouples 
which give the temperature values in the IPTS. If at 630 °C the difference 
between the true temperature and its value in the IPTS is known, the 
pyrometric method permits determining the corresponding difference at 
1064 °C. By apphcation of the same principle, the study has been extended 
to the temperature of the freezing point of silver and to several inter- 
mediate temperatures between 630 °C and 1064 °C. The use of an odd 
number of intermediate temperatures constitutes moreover a useful vari- 
ant in the study of the freezing point of gold; it permits the comparison of 
the luminances at 630 °C and 1064 °C of the same radiating cavity, which 
eliminates the effect of possible dissimilarities between the two cavities. 



S 







> 


Pi 




02> 


< \ 




;P3 

R 






















1 








D2 






E 
E 
o 

O) 


c 1 

















70mm 



Fijiuie 6. Pyrometric determination of the freezing point of fiold; tiie optical measuring 
device. Mi, aluminum coated quartz mirror: Oi. O2, Os, O4 objectives; L, field lens; Di, D2 
diaphragms; F, interference filter: R, detector: C, aperture of the blackbody cavity; S, mer- 
cury vapor lamp, M;, retractable mirror. 

The detector R (photoelectric tube of very good linearity) observes alternately the cavity 
at 630 °C and that at 1064 °C; the centering of the cavity is satisfactory when the green light 
spot furnished by the ensemble S, O4, M2 completely enters the aperture C of the cavity in 
question; this adjustment is verified with the aid of M.). 



132 



By this approach, the ratio of luminances, which is of the order of 150 for 
the direct comparison, is lowered to 12, or even less, which facihtates its 
measurement; on the other hand, there is no longer only one ratio to be 
determined, but several. 

The current work is distinguished fn^n similar determinations in 
several respects. First, we have obtained an emissivity very close to unity 
for the radiating cavities (fig. 7), by hollowing out in blocks of pure nickel, 
cavities having a very high "effective surface/aperture" ratio (above 700); 
next, we have used techniques perfected in the course of other work to 
develop ovens of very high stabihty and very good temperature uniformity; 
finally, we have chosen interference filters to isolate the desired spectral 
band (half-width from 8 to 15 nm). 

The difficulties encountered are essentially due to the thermocouples 
and interference filters; the former do not permit temperature verification 
to better than 0.1 K; the latter are hkely to give very weak residual trans- 
mission over very broad spectral ranges outside the useful transmission 
band, and these effects are difficult to evaluate with precision. 

The results obtained, in good agreement with those of other laborato- 
ries, show that the IPTS-68 is not a satisfactory representation of ther- 
modynamic temperatures in the range 630-960 °C; on the other hand, the 
temperature interval between the freezing points of silver and gold seems 




Figure 7. Pyrometric determination of the freezing point of gold: view of the interior of a 
radiating cavity. From left to right, the cover, the cylinder, and the base. The internal wall 
of the cavity is grooved and cross-ruled to increase the surface/opening ratio, and the bot- 
tom is slightly inclined to diminish the loss of radiation by specular reflection. At the center 
of the cover, one sees the aperture (10 mm diameter). 



133 



to be correctly evaluated (fig. 8). But the problem is much more general [4] 
and much work remains to be done to render the measurements more ex- 
act, in particular at very low and very high temperatures. 



873 
I 



973 
I 



K 

+ 0,5 



-0,5 



Reference 

_ (630,74 °C) 



1073 
I 



1173 



1273 
i__ 



1373 K 
I 




600 



700 



800 



900 



1000 



iioo°c 



Figure 8. Pyiometric determination of the freezinij p<iint of gold: results obtained. The curve 
gives from 630 to 1064 °C, the difference between the thermodynamic temperature and the 
temperature in the IPTS-68. One accepts by hypothesis that the temperature 630.74 °C in 
the IPTS-68 is exact and the c-i. Planck's second radiation constant, has the value 0.014 388 
m- K. The precisions of the freezing points of silver and gold are 0.13 and 0.16 K 
respectively. 



Bibliography 



[1] Guillaume, Ch.-Ed., Etudes thermometriques. Travaux et Memoires B.I. P.M. 5, 251 
pages (1886). 

Chappuis, P., Etudes sur le therniometre a gaz et comparaison des thermometres a 
mercure avec le thermometre a gaz, Travaux et Memoires B.I. P.M. 6, 312 pages (1888). 
Chappuis, P., Nouvelles etudes sur les thermometres a gaz, Travaux et Memoires 

B. I. P.M. 13. 66 pages (1907). 

[2] Echelle Internationale Pratique de Temperature de 1968, Comptes Rendus 13'' 

C. G.P.M.. 24 pages (1967); Comite Consultatif de Thermometrie. 8th session, pp. Al- 
A24(1967). 

[3] Bonhoure, J., Temperature du point de C(mgelation de Tor. Comite Consultatif de Ther- 
mometrie, 9th session, pp. T84-T87 (1971). 

Bonhoure, J., Etude pyrometrique des temperatures comprises entre 630 °C et 1064 
°C, Comite Consultatif de Thermometrie, 10th session, a paraitre (1974). 
[4] Temperature. Its Measurement and Control in Science and Industry, 2 , 444 pages 
(1955); 3, 2500 pages (1962), Reinhold Publishing Corp., New York; 4, 2383 pages 
(1973), Instrument Society of America, Pittsburgh. 



134 



CHAPTER VII 



ELECTRICITY 



The BIPM took a very early interest in electrical measurements. As 
early as 1884, for example, at the request of the International Committee 
for Weights and Measures, J. R. Benoit constructed on behalf of the French 
Ministry of Postal and Telegraph Services, 4 prototypes of the legal ohm 
and about 15 secondary standards. At a time when the ohm was the re- 
sistance, at the temperature of melting ice, of a column of mercury of 1 
mm^ cross section and 106 cm length, its construction was essentially a 
matter of the measurement of length and bore of glass tubing; it was thus 
natural to entrust it to the specialists of the BIPM who were currently per- 
forming this kind of study on mercury thermometers of high precision. 
Much later, in 1907, it was the BIPM which calibrated and adjusted the 
tubes destined to realize for France the new ohm defined at Chicago in 
1893 (length: 106.3 cm; mass of mercury: 14.4521 g). 

Although this activity was known and appreciated, it was only in 1921 
that the 6th CGPM modified the Convention of the Metre of 1875 to extend 
the scope of the BIPM to the domain of electric units. 

This decision was implemented in 1927 by the 7th CGPM which 
created for this purpose a Consultative Committee for Electricity iCCE) to 
"advise the International Committee for Weights and Measures on 
questions relative to systems of measure and electric standards." 

The CCE defined in 1928, in the course of its first session, the func- 
tions which needed to be assigned to the BIPM. These were: 

— To establish a central secretariat for organizing a systematic 
exchange of standards and for assuring the synthesis of the results 
obtained by the national laboratories. 

— To establish a laboratory to which physical standards represent- 
ing the results obtained in various countries could be brought for 
precise comparisons. 

— To estabhsh a stock of reference standards and working stan- 
dards, with the installations necessary for the comparison of other 
standards with those of the Bureau. 

These recommendations, adopted by the CIPM in 1929, define the 
present mission of the BIPM in the domain of electricity. 



573-106 O - 75 - 10 



135 



Electric Units 



In 1908, the International Conference of London had noted the con- 
cern of physicists with making a very clear distinction between the defini- 
tions of the units and their material representations. 

At this time, the electric units called "practical" were defined in terms 
of the CGS electromagnetic units and comprised part of the "Practical 
system of units"; they were for example: the ohm which had the value 10'' 
CGS electromagnetic units of resistance, the ampere equal to 10^' CGS 
electromagnetic unit of current, the volt equal to 10" CGS electromagnetic 
units of potential difference. 

On the contrary, the representations of these units constituted another 
system called "International System,"' based on two material standards: 
the international ohm, the resistance offered to an unvarying electric cur- 
rent by a column of mercury of a mass of 14.4521 grams, of a constant cross 
section and of a length of 106.300 centimetres, at the temperature of melt- 
ing ice, and the international ampere, an unvarying electric current which, 
in a solution of silver nitrate in water, deposits silver at the rate of 0.001 118 
00 gram per second. 

After the London Conference, there were then two systems: 

— the CGS system, absolute but purely theoretical (with its practi- 
cal multiples and submultiples: ohm. volt, etc.). 

— and the international system permitting the reproduction of the 
units with the best precision possible at the time, and the assurance 
of uniformity of electrical measurements throughout the world. 

In 1908, the agreement between the two systems was satisfactory but, 
very rapidly, the progress of electrical metrology made annoying diver- 
gences appear. As early as its first session, in November 1928, the CCE 
therefore proposed to the CIPM to substitute for the international units, an 
absolute system derived from the CGS units, as soon as it would be possi- 
ble to "fix with the desired accuracy \\\e ratios between the absolute units 
and the international units of current, electromotive force, and resistance" 
[1]. 

In June 1939, the CCE judged that this accuracy had been reahzed and 
recommended the transition to the absolute units: but the world events that 
occurred several months later did not allow the CIPM to meet before 1946, 
and it was necessary to wait until that time for the CCE recommendations 
to be adopted [2]. 

In 1946, the CIPM fixed the date of 1 January 1948 for putting the ab- 
solute electric system of units into effect (in usage since then) and in- 
dicated the relation to be used for converting from the international units 



' This "Tnternational System." designated thus in 1893 by the Congress of Chicago to distin- 
guish it from the absolute CC.S System, should not be confused with the International System 
of Units (SI) adopted by the 11th CGPM (1960). 



136 



to the absolute units. It also gave definitions of the electric units; we recall 
below those of the ampere, volt, and ohm. 

— The ampere is that constant current which, if maintained in two 
straight parallel conductors of infinite length, of negHgible circular cross 
section, and placed 1 metre apart in vacuum, would produce between these 
conductors a force equal to 2 X 10 " MKS unit of force [newton] per metre 
of length. 

— The volt is the difference of electric potential between two points 
of a conducting wire carrying a constant current of 1 ampere, when the 
power dissipated between these points is equal to 1 watt. 

— The ohm is the electric resistance between two points of a conduc- 
tor when a constant potential difference of 1 volt, applied to these points, 
produces in the conductor a current of 1 ampere, the conductor not being 
the seat of any electromotive force. 

These decisions of the CIPM were ratified by the 9th CGPM in 1948 

[3]. 

Standards 

Although in the International System of Units (SI) the electric base 
unit is the ampere, the two units whose material representations have al- 
ways served jointly as the departure point for electrical measurements in 
all laboratories are the units of resistance and electromotive force; the ohm 
and the volt are in fact the units which we know how to reaHze and main- 
tain with the most accuracy. 

Resistance Standards 

To be completely defined these standards have four terminals: two 
current leads and two potential taps (fig. 1). The best quality standards are 
the standards of nominal 1 fl value developed by the national laboratories 
(fig. 2). They are constituted of a metallic wire of an alloy having a low tem- 
perature coefficient, for example, manganin (85% copper, 12% manganese, 
3% nickel); they should in fact have the least possible sensitivity to varia- 
tions of the ambient temperature and to the heating produced by the 
passage of the measuring current. This wire, of 1.2 to 1.5 mm diameter, is 
wound in the form of a double helix (to reduce the self-inductance) and 
carefully annealed to assure the stability of its resistance; it is placed in- 
side a hermetically sealed container filled with pure mineral oil or an inert 
gas. 



137 



The standards of good quality have a temperature coefficient between 
5 and 10 X lO'^/K in the neighborhood of 20 °C; their resistance may 
change slowly with time, but this change does not exceed 1 X 10~^ per year 
for the best standards. 



c 

o 



/ 



u 



R 



B 



C 

-o 



Fijiure 1. Dia<;rarn slmwiii}; the principle <if a staiidaid resistor: R = U/I. C, terminals for the 
current feed: I', potential taps. To measure such a resistor it is necessary to use an arrange- 
ment which allows elimination ot the effect of the resistances in arms AC, BC. AP. and BP. 




Fifiure 2. Resistance standards of 1 il developed hy national laboratories. To insert a stan- 
dard into the measuring circuit, terminals C are set in cups filled with mercury (for the third 
standard to the right, one can also clamp wires under the terminals C ). Terminals P serve 
in the measurement of the voltage ilrop which results from the passage of current through 
the resistor. 



1.38 



Standards of Electromotive Force 



The volt is "maintained" by means of cells — or elements — of the satu- 
rated cadmium sulfate type (developed by Weston in 1893), whose elec- 
tromotive force at 20 °C is of the order of 1.01860 V. These cells belong to 
the category of elements called "reversible," each of the electrodes being 
immersed in an aqueous solution of a salt of the metal which constitutes 
the electrode (fig. 3). 





Figure 3. Cadmium-sulfate standard cell. Negative limb: A. cadmium amalgam in 2 phases: 
Positive limb: B. pure mercury: C. mercurous sulfate HgiSO,; E. saturated solution of cad- 
mium sulfate: D, crystals of cadmium sulfate CdS04 • 8/3 H>0. 



139 



The Weston element is a frajiile standard; it is sensitive to shock, 
vibration, and li^ht; a reversal is fatal to it. But it is especially sensitive to 
temperature variations which render its use ticklish. 

The electromotive force of a saturated Weston element decreases 
about 40 ixV when its temperature increases by 1 degree, in the neighbor- 
hood of 20 °C; furthermore it varies by 330 /jlW per degree of temperature 
difference between the two limbs. For the electromotive force of a standard 
cell to be defined to about 10 ' V, it is thus necessary that its temperature 
be known in absolute value to about 2.5 mK and that the temperature of its 
two limbs be equal within about 0.3 mK. 

The Weston element also has a serious defect as a standard: not only 
does its electromotive force require several weeks to stabilize after a tem- 
perature change, but in general it does not recover exactly its initial value 
when the initial temperature is reestablished. Only a few very well 
equipped laboratories can thus achieve a high stabiHty: a microvolt per 
year or even several tenths of a microvolt per year for the most successful 
elements. 

Installations of the BIPM 

The study of typical standards for the ohm and the volt comprises the 
basic experimental activity of the BIPM. To carry out this study and to 
maintain the standards under the best conditions, the BIPM has put vari- 
ous installations into more or less perfect running order. 

Kelvin Double Bridge 

A Kelvin double bridge (figs. 4a and 4b) is used for determining the dif- 
ference between two resistance standards; this instrument in fact, allows 
eliminating the influence of contact resistance, of current leads, and of the 
potential taps of the measured standards. 

The standards are compared in turn and repeatedly to a "tare re- 
sistance" whose value is adjusted by means of a shunt to obtain bridge 
balance (null current in the detector). 

The standards are kept in a bath of mineral oil. During the measure- 
ments this oil is kept in motion by an impeller, to remove the energy dis- 
sipated in the standards and in the tare by the measuring current (0.1 A). 

The comparisons are carried out at ambient temperature (20 ±0.05) 
°C; the exact temperature of each standard is registered to a few 
thousandths of a degree by means of mercury thermometers calibrated at 
BIPM. To eliminate the effect of possible parasitic electromotive force, 
bridge balances are obtained for the two directions of current. 

The installation at the BIPM permits determination of the difference 
between two 1-fi standards to about 1 X 10 " fl. 



140 



A 

-AA/WVW 



C 

■AWVIW 




B 

mm- 



D 

wvwv- 



T 



Figure 4a. Diagram showing the principle nfthe Kelvin double bridge. Wiien there is no cur- 
rent through tiie detector G. one has tiie relation: 

XIT = AIB = CID 

X. standard to be compared: T. tare resistance. 



141 



p 



A 

^ — mmr 



B 

■A/WWW — ^ 



0 



D 



r— A/VWWV — ^^VWVW-n 




^AAAAA/V 

X 



-3 

-AAAAr 

^4 



N 



T 

^lAAAAMr 



K 



If y 

Figure 4b. Diagram of the double bridge used at the BIPM. X. standard to be compared: T. 
tare resistance (1.007 fl): S. 6-decade resistance box (resolution: 0.1 11): A. B. C. D principal 
bridge resistances (nominal value: 100011): P and N, switches: K. current reversing switch: 
61. e-2. e:j. 64. resistances of the arms of standard X and of the connections (the influence of 
these parasitic resistances is eliminated by establishing auxiliary balances, the first with P 
and N closed with adjustment of s across the terminals of a. the second with P and N open 
and with adjustment of s' across the terminals of c). The principal double bridge cor- 
responds to P open and N closed: it is balanced with adjustment of S. If Si and S2 are 
respectively the values needed for S to obtain bridge balance with two standards Xi and X2 
the difference between these two standards is given by: 

X, - X;= (AIB) ( -I^-J^^ I 

If the ratio .4/Bof the arms of the principal bridge, nominally equal to I. is in tact equal 
to (1+S). the difference (A'l — ^"2) is determined with a relative error equal to 8. By in- 
terchanging the arms A and B in the middle of the comparison of the two standards — 
^¥2, the relative error of the difference is reduced to 6-/2. 



142 



Potentiometer 

To determine the difference of electromotive force between two cells, 
they are connected in opposition and the resulting electromotive force 
measured by means of a potentiometer. The voltages to be measured are 
thus always small (at a maximum, several hundred microvolts) and relative- 
ly easy to determine with precision. The device used at the BIPM essen- 
tially comprises two potentiometers connected in series (fig. 5); the first. A, 
serves to regulate the potentiometer current (10~* A), the second, B, to 
measure the difference between the electromotive forces of the two cells to 
be compared. 

For a null detector, we use a galvanometer amplifier whose principal 
advantage is to avoid discharging the cells during measurement. 

The BIPM potentiometer allows determination of the difference 
between two cells to a few tens of nanovolts. 




Figure 5. Diagram of potentiometer used to compare two standard cells. X| and X2. cells to be 
compared, connected in opposition: Ki. reversing switch to give the appropriate polarity to 
the potential difference to he balanced against {Xi — X->): ¥.■>. double reversing switch for 
simultaneously reversing the sense of the potentiometer current and the polarity of the 
measured vohage {Xi — X-i), for ehminating the effect of possible parasitic electromotive 
forces in the circuit of the balance detector (',■,■ The potentiometer current /. is iurnished by 
a battery of dry cells P and is not interrupted. Before each measurement its value is ad- 
justed to 1 X 10"'* A; for this, the potentiometer (A) is set to the known value of electromo- 
tive force of a standard ceil W and the rheostat Rh, is adjusted for a null on the galvanome- 
ter Gi. When /i = 10"^ A. the terminals of the potentiometer (B) supply a potential dif- 
ference which is adjustable from 0 to 1600 /xV in steps of 10(U,V. To establish the balance 
(null current in the detector G2), we add algebraically to (A^i - X-i) the potential difference 
created at the terminals of a 1-fI resistor R by the passage of a current l> measured by 
means of the microammeter 



143 



Oil Bath for Storage and Measurement of Cells 



The BIPM stores and measures its reference cells in a tank filled with 
mineral oil (fig. 6). It is also in this tank, which can hold 120 cells, that are 
immersed the transport cells which participate in the international com- 
parisons and the cells which the BIPM receives for calibration. 

The heat capacity of the oil reduces the temperature fluctuations. It 
permits obtaining, as quickly as possible, thermal equilibrium of the cells 
which are sent to the BIPM. During measurement, the rotation of an im- 
peller assures a radial circulation of the oil whose temperature uniformity 
is thus obtained to better than 5 X 10"'* K throughout the bath. 

In the course of a measurement, which lasts around a half-hour, the 
temperature rise produced by the agitation of the oil is of the order of 
1.5 mK. 

This bath is not temperature regulated but it is placed in a room kept 
at (20 ±0.05) °C. Its temperature is determined by means of one or sev- 
eral platinum resistance thermometers. It is closed by a cover of opaque 
Plexiglas. 




Figure 6. Mineral-oil hath in which the standard cells are stiired and measured. Ch. rack sup- 
porting the standard cells (each rack can rotate a half-turn about its vertical axis X); P. posi- 
tive terminal (the negative terminals are connected to each other): PL. Plexiglas partition 
separating the tank into two compartments: H, impeller assuring circulating of the oil, 
which passes from the upper comijartment to the lower compartment, comes back up 
through the peripheral orifices 0. and is then channeled toward the center of the tank by the 
lateral faces of the racks. 



144 



The racks which carry the cells are mounted on supports which can 
turn about a vertical axis. By rotation of a half turn the cells placed at the 
periphery are carried to near the center (and conversely) and the positions 
of the limbs of each cell relative to the flow of oil are interchanged. The ef- 
fects of possible temperature gradients are thus eliminated. 

Temperature-Regulated Air Enclosure 

To maintain the cells at a temperature still more constant and more 
uniform than in the oil bath, the BIPM has constructed a temperature-regu- 
lated air enclosure whose thermal behavior is being studied. This enclosure 
comprises cubes, some of thin duralumin walls, others of thermally insulat- 
ing walls of expanded polystyrene, stacked one within the other (fig. 7). The 
innermost cube which contains the cells (distributed in 16 massive duralu- 
min blocks) is of copper with thick walls to have a large heat capacity. 

This enclosure is placed in the same room, controlled at 20 °C, as is 
the oil bath; it is maintained at about 21 °C by electric heating of 10 W 
uniformly distributed on the six faces of the next to the outer metallic cube. 
Its temperature is regulated by a mercury thermometer with a contact and 
is measured by means of two 100-fl platinum probes, a thermistor bridge, 
and two copper-constantan thermocouples lodged in the middle partition 
of the interior chamber. 

To reduce possible heat exchange between the cells and the exterior, 
the conductors which lead to the cell terminals are teflon insulated multi- 
strand copper cables of very small cross section (0.014 mm^), very long 
(about 4 m), and wound in a spiral. 

Periodic International Comparisons 

To assign values to the resistance standards and standard cells which 
constitute their reference groups, the principal national laboratories carry 
out absolute determinations. These are electromechanical experiments 
which relate the electric units to the units of length, mass, and time in con- 
formity with the definition of the ampere. These are difficult measure- 
ments, long and costly, which must, it is well understood, be repeated 
periodically; their precision is. for most of the electric units, inferior to the 
stability of physical standards which represent these units, and to the com- 
parison measurements between these standards. For these reasons, and for 
reasons of continuity, the national laboratories do not modify the values of 
their reference standards each time they carry out absolute determina- 
tions. They do this only exceptionally, practically in the three following 
cases: 



145 




Fijiure 7. Tempei ature-ret:ulatf d air enclosure for storing cells. Cu. interior cube of copper 
with its middle partition enclosing the platinum probes, thermistors, and thermocouple 
junction which permit knowing the temperature of tiie cells; D, duralumin cubes: P. ex- 
panded polystyrene; B. duralumin blocks which can each hold six cells; C, cover for a 
block. 



146 



— When the difference between the resuh of the new determina- 
tion and the value previously assigned exceeds the uncertainty of 
the measurements, and when some particular reasons can explain 
an abnormal change in the material standards (bad storage condi- 
tions, for example), 

— When the progress of metrology permits improving the precision 
of the absolute determinations (this has been the case for several 
years for the farad and the ohm), 

— To improve international uniformity (as was the case for the ohm 
and the volt the 1st of January 1969). 

The reference groups maintained in various national laboratories com- 
prise only approximate representations of the units (ohm and volt). 

One of the essential tasks of the BIPM consists in determining the 
spread among these representations: it is the object of the international 
measurements in the world. These comparisons also permit evaluation of 
the effective precision obtained in the absolute determinations and can 
lead to the discovery of possible systematic errors. 

To participate in these periodic comparisons (biennial from 1932 to 
1957, then triennial since 1957). all the laboratories invited by the CIPM 
simultaneously submit several standards of resistance (of 1 fi) and of elec- 
tromotive force (Weston cells) to BIPM. The transportation of Weston cells 
requires elaborate precautions; laboratories most often utilize Cardan 
suspensions to keep them vertical (fig. 8) and transportable temperature- 
regulated enclosures to avoid all thermal shock. 

With the development of high-precision metrology throughout the 
world, the number of participants in the international comparisons con- 
tinues to grow. In 1932, the first comparisons had assembled at the BIPM 
20 standard cells and 81-0 resistors provided by 4 laboratories. 

In 1973, 11 laboratories sent to the BIPM 59 bare cells (in 10 groups), 
37 cells at 30 °C (in 9 temperature-regulated enclosures), 36 l-O resistors, 
and for the first time, 15 resistors of 10^ (1. The duration of the measure- 
ments has a parallel growth; those of 1973 lasted about 4 months. 

Given the large number of standards, it is not possible, also not useful, 
to compare them two by two in all possible combinations. We therefore 
adopted some simplified comparison schemes; an example of comparison 
of resistance standards is reproduced in figure 9. 

For resistors as for cells, each measurement is made twice, at times 
which are symmetrical relative to the central date of the comparison, to 
eliminate in the first approximation the possible drifts of the standards. 



147 



Figure 8. Sliippiiij: case witli Cardan suspension for the transpDrtation of cells by freight. The 
box B which holds the cells remains vertical during transport. A. accelerometers recording 
niaximuni acceleration (shock, in particular); C, recorder for oscillations (a second recorder 
is invisililc in this photograph). 



148 




Figure 9. Example of tlie eompaiisoii scheme for l-fi resistance standards. For comprehen- 
sion of the scheme, tlie first cokimn has been repeated on the riglit in broken lines, and the 
first row repeated at the bottom. The standards of the BIP.M are identified by double cir- 
cles. The standards of a given laboratory are compared among themselves in all possible 
combinations (comparisons indicated by heavy lines). This scheme, used in 1973 to com- 
pare 42 standards, needed the execution of 198 comparisons (99 comparisons "going" and 
99 "returning"). 



149 



Results of the Comparisons 



The results of measurements carried out at the BIPM express the 
value of the transport standards of national laboratories in terms of the 
representations of the ohm and the volt maintained by the reference groups 
of the BIPM. 

Before their trip to the BIPM and after their return, the transport stan- 
dards are carefully caUbrated in their laboratory of origin; thus it is verified 
that they have not been subject to any damage by reason of their transport, 
and their probable values are calculated for the central date of the mea- 
surements made at the BIPM. 

In comparing the two values attributed to the transport standards for 
the same date, we deduce the divergences between the representations of 
the units maintained by the national laboratories and those which are main- 
tained by the BIPM. 

Figures 10 and 11 show the relative changes, since 1950, of the 
representations of the units of resistance and of electromotive force main- 
tained by the national laboratories. 



() 



+ 17.9 




♦ 22 




120,9] 


1 16.9 


0 




6 




0 1 


0 




1960 



1965 



1970 



Figure 10. Results of the periodic comparisons of national resistance standards, from 1950 to 
1973 (difference between the reference values maintained by the national laboratories and 
that of the BIPM). In 1957, the ASMW reduced the value of its national reference by 16.9 
/xH to adjust it to that of the BIPM. To achieve a better international uniformity, the PTB, 
the NSL, the NRC, the LCIE, and NPL adjusted the values of their rational references to 
that of the BIPM on the 1st of January 1969. B NPRL;0ASMW:#P'1'B:VNSL;ANRC; 
□ NBS;BLC1E:+IEN; * ETL: X NPL: x IMM 



150 



I 22.3 
M 





0 

T-10.2 



1955 



1970 



Figure 11. Results of the periodic comparisons of national standards of electromotive force, 
from 1950 to 1973 (difference between the reference values maintained by the national 
laboratories and that of the BIPM). On .lanuary 1, 1969. the reference maintained by the 
BIPM was reduced by 11 x 10 " to put it into closer agreement with the volt. On the same 
date all the national laboratories, except the ASMW, also corrected their national 
references to make them coincide with the new reference of the BIPM. For tiie identifica- 
tion of the signs, see figure 10. 



Maintenance of the Ohm and the Voh by the BIPM 

As do also all the national laboratories, the BIPM maintains the ohm 
and the volt by means of 1-fl resistance standards and saturated cadmium 
sulfate cells. The majority of these standards (especially resistors) were 
fabricated by various national laboratories and deposited at the BIPM in 
accordance with the recommendation of the CCE (1928) approved by the 
CIPM. Currently, 6 1-fl standards and 43 cells constitute the reference 
groups of the BIPM. It is by comparison with these references that the 
BIPM determines the value of standards which are submitted to it for 
study. 

What do the references maintained at the BIPM represent? 

Until 1935, these references, identified by the symbols 0^ and 
were the averages of material representations of the ohm and the volt in 
use in the national laboratories which had participated in the most recent 
periodic international comparisons. They could consequently vary on the 
occasion of each comparison; it sufficed for this that a new laboratory came 



573-106 0 - 75 - 11 



151 




152 



in or tliat one ot tlie old ones modified tlie value assijined to its referenee 
standards in the interval between two comparisons. 

To avoid this serious drawback, the CCE in 1935 defined the "mean 
international ohm" (Hm) and the "mean international volt" (Vm), as the 
means, on 15 March 1935 and on 4 December 1934. respectively, of the 
representations of the ohm and the volt maintained in the six lar<ie national 
laboratories of the time (PTR. NBS. LCE. RTL. NPL. and IMM), these 
means to be considered henceforth as constant. These are the means VL^ and 
Vm which the BIPM maintained from 1935 to the 1st of January 1948. date 
of the transition to absolute units. 

It was foreseen that the value of the standards of the BIPM would be 
readjusted, when necessary, on the occasion of international comparisons 
(and this was actually the case in 1935. 1937. and 1939); but starting in Sep- 
tember 1939 the BIPM found itself isolated and was forced to maintain Hm 
and Vm depending solely on the quality of its own group of reference stan- 
dards. Some later studies have shown that the behavior of these standards, 
kept under the best possible conditions, had been excellent; and this was 
fortunate for they played an important role in 1946. In fact, between 1939 
and 1946. several reference standards of the six national laboratories in- 
volved were destroyed or damaged. It was thus considered in 1946 that the 
"international mean units" Om and V^ were those maintained by the stan- 
dards of the BIPM. The relations then adopted by the CIPM to pass from 
these units to the absolute units were therefore applied directly to the 
references maintained by the BIPM which became, starting on 1 January 
1948. figiPM (absolute ohm maintained by the BIPM resistors) and VgipM 
(absolute volt maintained by the BIPM cells), with the transformation rela- 
tions given in table 1. 

In 1946. the CIPM decided that henceforth Hbipm and Vbipm would con- 
stitute autonomous references and would participate in the international 
comparisons on the same basis as the references of the national laborato- 
ries. Since 1950 the results of the international comparisons have been ex- 
pressed in terms of the references maintained by the BIPM. 

The CIPM also specified in 1946 that "the values to be assigned to the 
reference standards maintained by the BIPM would be fixed from time to 
time by the CIPM on the advice of the CCE, in accord with the results of 
the comparisons carried out between these standards and the national 
standards whose values had been determined directly by absolute measu- 
rements. Conforming to this decision, the CIPM decided in 1968 to correct 
the values assigned to the references of BIPM. To avoid confusion between 
the old references and the new ones, the symbols have been modified. 

The relations between the references successively maintained by the 
BIPM are given in table 1. 

Most of the large national laboratories having simultaneously 
proceeded to the readjustment of the values assigned to their reference 



153 



standards, cuncoidance ainonji the national representations of the ohm and 
the volt was assured for the first time to about one part in a million, practi- 
cally throujihout the entire world, the 1st of January 1969. 

Progtress of Metrolof?y in the Field of Electrieity 

After having been very slow and laborious for numerous years, being 
limited to the refinement of relatively old classical methods (use of the cur- 
rent balance to realize the ampere, calculation of self-inductance or mutual 
inductance to realize the ohm), the progress of electrical metrology has 
been remarkable since 1956; thanks to the application of recently 
discovered physical laws, the verification of the permanence of standards 
and the accuracy of the realizations of the units have been considerably im- 
proved. 

Permanence of Standards 

Up until about 1960 for the ohm and 1970 for the volt, it was difficult to 
detect the drift of national reference groups. The relative drifts placed in 
evidence by the international comparisons indeed seemed to prove the in- 
stability of the standards, but the limited precision of absolute measure- 
ments (20 to 50 times less precise than the relative measurements) did not 
permit determining this instability with assurance. 

Resistors of Pure Metal 

To attempt the determination of the instability of manganin resistance 
standards which comprised its reference group, the BIPM has constructed 
several l-fi standards of platinum wire, defined at the temperature of the 
triple point of water. From very numerous comparisons carried out regu- 
larly from 1958 to 1969 between the standards made of manganin and of 
platinum, the BIPM has concluded that its reference group probably 
remained stable to about 5 X 10"' fi. 



Gyromagnetic Ratio of the Proton 

It has been known for several years, how to reproduce the ampere with 
a good precision (about 10 with the aid of the phenomenon of nuclear 
magnetic resonance. 

For a proton (nucleus of hydrogen) of magnetic moment fx placed in a 
field of magnetic flux density B, there exist only two possible energy states: 



154 



/jlB when its magnetic moment is parallel to B and — /jlB when it is an- 
tiparallel. When the proton passes from one state to the other, its energy 
thus changes by 2fjiB, which involves the emission or absorption (according 
to the sense of the flip) of a quantum of radiation hv = 2ixB (h, Planck's con- 
stant; V, radiation frequency). The frequency of the radiation is propor- 
tional to B: v={2/jijh) B; the proportionahty factor y = (2/x//i) is called the 
gyromagnetic ratio of the proton [4]. If the flux density B is created by a 
current / in a solenoid, it is expressed by B = kl and consequently v= kyl. 
The phenomenon of nuclear resonance then permits directly relating a cur- 
rent / to a frequency which is well defined and easy to measure. If A" 
remains constant (that is to say, if the geometric dimensions of the solenoid 
and the permeability of the medium do not change), it is sufficient to 
reproduce v to recover /. 

Experimentally, the nuclear magnetic resonance of a very large 
number of protons is observed at the same time; besides, the larger this 
number is, the more convenient is the measurement. As it is necessary, 
however, to contain these protons in a small volume (in the region of space 
where the flux density is uniform), one observes in practice the nuclear 
resonance in a sample of pure water of several cubic centimetres (6 X 10-- 
hydrogen atoms per cm'*) which has been placed at the center of a long 
solenoid. 

At the BIPM, we do not yet use the phenomenon of nuclear magnetic 
resonance to maintain the ampere but we use it to stabilize and measure 
the magnetic flux density in the air-gap of the electromagnet where we 
determine the energies of a-particles (see p. 190). 

Application of the Josephson Effect 

To monitor the behavior of its reference cells, the BIPM has un- 
dertaken to put the Josephson effect into operation. The phenomenon, 
discovered in 1962 [5], manifests itself between two superconductors 
separated by an insulating layer of very small thickness (1 to 3 nm) con- 
stituting a "Josephson junction"; it furnishes a relation between a direct 
voltage and a frequency. 

In a superconductor, the conduction electrons of opposite spin group 
themselves by pairs (Cooper pairs). These pairs of electrons do not obey 
the same statistics as do independent electrons; they have a tendency to 
put themselves into the same quantum state so that a single wave function 
<^ = (/)()e'^ (called the order parameter) suffices for characterization. As a 
result, one can observe a quantum effect on the macroscopic scale. 

When the insulating barrier which separates two superconductors is 
sufficiently weak that the phases d-z and of the order parameters ap- 
propriate to each of them cannot vary independently, some electron pairs 



15S 



can cross the barrier by the tunnel effect. The current / which resuhs, and 
the time variation of the difference between the phases have for their ex- 
pression: 

/=/csin(6>2 - ^i) (1) 

and 

d{d,-9,) _2e (2) 
dt h 

where 

/c = critical current whose value depends mainly on the nature of the junc- 
tion and on the magnetic field in which it is placed, 
e = elementary charge 
h — Planck's constant 

U = potential difference across the terminals of the junction. 

If one passes a bias current / through such a junction, the phases di 
and 62 adjust themselves to satisfy equation (1) and no voltage appears at 
the terminals of the junction as long as / ^ /c (this is the d-c Josephson ef- 
fect). When / becomes greater than /g a voltage U appears and the dif- 
ference between the phases {62 — Bi) increases proportionally with the 
time; by this fact the junction becomes the seat of an alternating current of 
frequency v = {2elh) U (this is the a-c Josephson effect which relates Uio v 
through the natural constants e and h). 

If the bias current / is progressively increased while the junction is ir- 
radiated with an electromagnetic radiation of frequency v, the voltage U 
across the terminals of the junction increases discontinuously and exhibits 
steps whose levels are multiples of hl2ev (figs. 12a and 12b). With the value 



A U 



























Figure 12. A-c Josephson effect, a: theoretical characteristic U = f {\) =n(hvj2e)\ b: 
characteristic observed in the neighborhood of the 250th step (about 5 mV); step width in 
current, about 20 /xA. 



156 



2e/A = 483 594 GHz/V and for a frequency of incident radiation ^' = 9.67 
GHz. the steps are equidistant in the neighborhood of 20 /jlY. 

The relation £/=n(/i/2e)f is independent of the nature of the super- 
conductors and the barrier, of the temperature, of the magnetic field, and 
of the power of the incident radiation. 

The Josephson voltages are however always small (no more than a few 
millivolts), thus difficult to measure with high precision. They are neces- 
sarily produced at a very low temperature (4.2 K or less), while the cells to 
which they are to be compared are maintained at 20 °C (293 K) or 30 °C (303 
K); thermoelectric voltages necessarily result, whose influence must be 
eliminated as completely as possible under pain of introducing systematic 
errors into the measurements. Finally, the precision of the comparison de- 
pends directly on that of the voltage comparator. 

At the BIPM, we fabricate junctions Pb - PbxO„ - Pb or Pb - 
AljOy — Pb (fig. 13) (barrier resistance 200 to 300 mfi: step height, 50 to 
100 ^A), with which we can produce conveniently usable Josephson volt- 
age of 5 mV (for example, the 250th step). We put two junctions in series to 
finally make available a voltage of 10 mV. 

The voltage comparator reahzes to about 1 X 10"** the 100/1 ratio which 
exists between the electromotive force of the cell under study and the 
Josephson voltage. It is constituted of 2 "Hamon devices" [6] placed in se- 
ries and each comprising 10 lOO-H resistors; the 10 resistors of the first 
device are connected in parallel (resulting resistance 10 fl) when the 10 re- 
sistors of the second are connected in series (resulting resistance 1000 Cl) 
and conversely. 

J J J J 



a 




I \ 1 

0 1 2 cm 

Figure 13. Small glass plate tarrying four Josephson junctions. J. junction: I'b. lead: a. sol- 
dering points for current and voltage leads. 



157 



We eliminate the effect of thermal electromotive forces by repeating 
the measurements after having reversed the bias current through the junc- 
tions, the current m the comparator, and the polarity of the cell under 
study. 

A diagram of the principle of the installation at the BIPM is given in 
figure 14. This installation is placed inside a screened room to shield it 
from stray electromagnetic radiation. 

The cells which are compared to the Josephson voltage are maintained 
in the temperature-regulated enclosure at 30 °C located in the screened 
room and they are periodically calibrated relative to the BIPM reference 
cells. 

During the measurements, the temperature of the helium bath in 
which junctions are immersed is lowered by pumping to about 1.5 K. Below 
the lambda point (2.17 K) the helium in fact becomes superfluid and its 
thermal conductivity exceptionally high (200 times better than that of 
copper); the uniformity of the bath temperature is considerably improved 
and the loss of helium reduced. 

The microwave-frequency electromagnetic radiation is furnished by 
a klystron where frequency is held constant to a few parts in 10^ throughout 




Figure 14. Diagram of the principle of the installation for the comparison of the Josephson 
voltage with the electromotive force of a standard cell. A. source of constant current for the 
voltage comparator; B. source of bias current for the junction; C. voltage comparator; J, 
junction; W. standard cell (electromotive force E): Ii, I2, I.3 current reversers; d. G2. G3, 
balance detectors; H.F., source of microwave radiation (K, klystron; P, controlled supply 
for the klystron; S. frequency stabilizer; CF, frequency counter; EF, frequency standard). 
At balance (null current in G, and G2) the potential difference across the junction terminals 
is equal to £'/?2/^ii. 



158 



the whole measurement by a stabiHzer which acts on the polarization volt- 
age. The frequencies used are of the order of 8.5 GHz for the Pb-Pb^Oy-Pb 
junctions and of 9.5 GHz for the Pb-Al.rO„-Pb junctions, and the irradiation 
power is in the neighborhood of 200 mW. 

The frequency counter is calibrated by means of a quartz clock, itself 
calibrated starting from the 200 kHz transmissions of the station at Droit- 
wich (United Kingdom). The measured frequencies are known to about 1 X 
10-". 

The BIPM continues to maintain the volt by means of standard cells, 
but the electromotive force of these cells is periodically redetermined by 
comparison with the reference voltage of a Josephson junction. We hope to 
thus be able to assure the permanence of the unit of electromotive force 
maintained by the BIPM to about 1 X 10"^ V. 

Accuracy of Realization of the Units 

Although the BIPM does not carry out absolute measurements, it very 
closely follows the results and advancements of measurements made in the 
national laboratories; these results in fact enter into the international com- 
parison and serve to fix the values of the BIPM reference standards; as to 
advancements, they guide the future activities of the BIPM. 

Unit of Resistance 

A very important advance has been realized in the determination of 
the farad and, as a consequence, in that of the ohm. Three reasons have 
combined for this advance. 

The first and essential reason was the discovery in 1955 by A. M. 
Thompson and D. G. Lampard, of the NSL (Australia), of a new electro- 
static theorem [7] permitting rigorously the reduction of the determination 
of the capacitance of a capacitor of appropriate type to the determination 
of a length, assuming the permittivity of space, eo, known. In the most 
highly perfected apparatus [8], the length to be measured is that of a dis- 
placement; it is determined by interference measurements in terms of the 
standard radiation of krypton 86 with a precision around 1 X 10^**. 

There was next the development of transformer comparator bridges 
[9] thanks to which one can pass from very small capacitances (0.25 to 0.50 
pF) determined in absolute value to capacitances of practical value (up to 
0.1 fiF) without loss of precision. 

There was finally, more recently, the new determinations of the speed 
of light to about 4 X 10--' (c = 299 792 458 m/s) [10] , from which is deduced 
the permittivity of space by the relation eo = 10^/47rc^. 



159 



The conjunrtiDii of these three advances today makes the farad, for- 
merly without metrological interest, the eleetric unit best known in ab- 
solute value. It is thus the farad, and no longer the henry, from which one 
now derives the value of the ohm through the intermediary of a frequency. 
The precision thus obtained is in the neighborhood of 1 X 10 it has been 
improved by a factor of 30 in about 15 years. 

The interest in capacitors of small value is such that they will 
probably, in the near future, be objects for international comparisons of the 
same kind as standards of resistance and of electromotive force. The BIPM 
has consequently equipped itself for carrying out comparisons of capaci- 
tors of 1 , 10, and 100 pF with a precision of about 1 X 10~**. 

Unit of Electromotive Force 

The absolute determination of the volt has similarly profited from the 
advances made in the determination of the farad. The possibility of replac- 
ing the always difficult and uncertain calculation of a capacitor by its mea- 
surement has given a fresh impetus to the so-called "absolute electrome- 
ter" in which the potential U applied to the movable member of a capacitor 
is deduced from the measurement of a force F and the variation 8C of the 
capacitance in terms of the relative displacement 8x of the movable 
1 8C 

member (F=-— C/'^). The precision of the determinations underway 
/ ox 

in several national laboratories could reach 1 x 10"'', that is to say, three to 
four times better than the precision currently obtained. 

Conclusion 

Following the mission which was assigned by the CIPM in 1929, the 
BIPM has for almost a half century assured the uniformity of electrical 
measurements throughout the world. Applying without delay the advances 
of science and technology, it has continually improved its installations or 
created new ones in order that its standards permanently represent the 
ohm and the volt as exactly as possible. In 1939, the CCE estimated that 
the uncertainty was 2 X 10~^ for the ohm and 1 or 2 X 10""* for the volt; in 
1948 these uncertainties were reduced to 1 X lO"'' for the ohm and 2 X 10~^ 
and a few in 10''. Progress has thus been continual. 

These successes have led several national laboratories to request the 
CIPM to extend the competence of the BIPM to measurements of electric 
quantities in the domain of radiofrequencies. The CIPM received this 
request favorably and in 1964 approved the creation within the CCE of a 
permanent working group for radiofrequency quantities. Without par- 
ticipating in the work experimentally, the BIPM has coordinated, since 
1965. the execution of several international comparisons carried out in this 
domain by the specialized laboratories. 



160 



The results already obtained are satisfactory and we believe that in 
this new discipline in full development, international collaboration will per- 
mit rapid improvement in the consistency and precision of measurement 
results. 

Bibliography 



[1] Proces-Verbaux C.I. P.M. 13, p. 58 (1929). 

[2] Proces-V erbaux C.I.P.M. 20, p. 129 (1945 1946). 

[3] Comptes Rendus 9'' C.G.P.M.,p. 49 (1948). 

[4] Purcell, E. M., Torrey. H. C, and Pound. R. V.. Resonance absorption by nuclear mag- 
netic moments in a solid. Phys. Rev. 69, pp. 37-38 (1946). 

Bloch, F., Hansen. W. W., and Packard. M., Nuclear induction, Phys. Rev. 70, pp. 
460-474(1946). 
[5] Josepbson, B. D.. Phys. Letters 1, p. 251 (1962). 

Langenberg, D. N., Scalapino, D. J., and Taylor. B. N., The Josephson effects. Scien- 
tific .American, pp. 30-39 (May 1966). 

Taylor. B. N., Parker, W. H., Langenberg. D. N., and Denenstein. A., On the use of 
the AC Josephson effect to maintain standards of electromotice force, Metrologia 3, 
No. 4, pp. 89-98 (1967). 

Petley, B. W. and Morris, K., A measurement of 2ejh by the AC Josephson effect. 
Metrologia 6, No. 2, pp. 46-51 (1970). 
[6] Hamon, B. V., A 1-100 fl build-up resistor for the calibration of standard resistors, J . Sci. 
Instr. 31, No. 12, pp. 450-4.53 (1954). 

Page, Ch. H.. Errors in the series-parallel buildup of four-terminal resistors, J. Res. 
Nat. Bur. Stand. (U.S.) 69C, No. 3. pp. 181-189(1965). 

Page, Ch. H., Errors in the series-parallel buildup of four-terminal resistors, J. Res. 
Nat. Bur. Stand. (U.S.) 69C, No. 3, pp. 181-189 (1965). 

Page, Ch. H., Tetrahedral junction error contribution to a series-parallel four-terminal 
resistor, IEEE Trans. Instrum. Meas. lM-23, No. 1, pp. 5-8 (1974). 
Harris, F. K., Fowler, H. A., and Olsen, P. T., Accurate Hamon-pair potentiometer for 
Josephson frequency-to-voltage measurements, Metrologia 6, No. 4, pp. 134-142 (1970). 
Finnegan, T. F. and Denenstein. A., High accuracy potentiometers for use with ten 
millivolt Josephson devices. I. Double series-parallel exchange comparator. Rev. Sci. 
Instr. 44, No. 8, pp. 944-953 (1973). 

[7] Thompson, A. M. and Lampard, D. G., A new theorem in electrostatics and its applica- 
tion to calculable standards of capacitance. Nature 177, p. 888 (1956). 
Lampard, D. C, A new theorem in electrostatics with applications to calculable stand- 
ards of capacitance, Proc. Inst. El. Engrs., Monograph 216M, 104C, 10 pages (1957). 

[8] Clothier, W. K.. A calculable standard of capacitance, Metrologia 1, No. 2, pp. 36-55 
(1965), 

[9] Thompson. A. M.. The precise measurement of small capacitances, IRE Trans, on In- 
strumentation 1-7, Nos. 3-4, pp. 245-253 (1958). 

McGregor, M. C, Hersh, J. F., Cutkosky, R. D., Harris, F. K., and Kotter, F. R., New 
apparatus at the National Bureau of Standards for absolute capacitance measurement, 
IRE Trans, on Instrumentation 1-7, Nos. 3-4, pp. 253-261 (1958). 
[10] Terrien, J.. International agreement on the value of the velocity of light, Metrologia 10, 
p. 9 (1974). 



161 



CHAPTER VIII 



PHOTOMETRY 



When, in 1875, the BIPM was created to look after length and mass, T. 
Edison had not yet constructed the first incandescent lamp. It was, how- 
ever, already a century and a half since P. Bouguer had pubHshed his Essai 
d'optique sur la gradation de la lumiere, which can without doubt be con- 
sidered as the first serious attempt at visual photometry; the luminous 
sources of that time were flames and even the name of the various units in 
use up to 1948 strangely recalls the first standards: candles. There have 
been successively lamps using coleseed oil (Carcel), pentane gas (Vernon- 
Harcourt), amyl acetate (Hefner); in all these cases the luminous intensity 
depended not only on the fuel, but also on the wick, the height of flame, etc. 
To avoid the inconveniences of flame standards, Violle proposed in 1879 to 
adopt the luminous intensity emitted from 1 cm- of the surface of a bath of 
pure platinum in the course of soHdification; unhappily, and for various 
reasons (impurities in the platinum, for example), VioUe's standard had low 
reproducibility. 

Artificial illumination became practical and effective only with the ap- 
pearance of the incandescent lamp with a carbon filament (1879) and the 
invention of the gas mantle (1895); it was the rivalry between these two 
sources that made photometry progress. 

Originally, each country had its own, and rather poorly reproducible, 
unit of luminous intensity; it was necessary to wait until 1909 to see a 
beginning of unification on the international level, when the national 
laboratories of the United States of America, France, and Great Britain de- 
cided to adopt the international candle represented by carbon filament 
lamps; Germany, at the same time, stayed with the Hefner candle, defined 
by a flame standard, and equal to about nine-tenths of an international can- 
dle. But a standard based on incandescent lamps, and consequently depen- 
dent upon their stability, would never have been fully satisfactory and 
could therefore be only provisional; on the other hand, the properties of a 
blackbody provided a theoretically perfect solution and, as early as 1933, 
the principle was adopted that new photometric units would be based on 
the luminous emission of a blackbody at the freezing temperature of 
platinum (2045 K). 



163 



It was in this situation, perhaps a little confused, but full of hope, that 
the CIPM decided in 1937 to extend the activities of the BIPM and to in- 
stall a photometric laboratory in the Pavilion de Breteuil, in order to "con- 
tribute to the international unification of the important physical quantity 
which is the unit of light." 

The role of the BIPM was not, and is no more so today, to realize the 
primary standard (blackbody), but to maintain secondary reference stan- 
dards for practical use in the form of standard incandescent lamps having 
carbon or tungsten filaments; the values assigned to these lamps were to be 
expressed with the aid of the "mean unit" that results from determinations 
made in all national laboratories that have realized the primary standard. 

Naturally, photometry is much more than the comparison of luminous 
sources. Associated with radiometry, its applications extend to many other 
disciplines such as colorimetry, optics, photography, astronomy, 
pyrometry, etc. But here as elsewhere, the role of BIPM is definite and 
voluntarily limited to the basic metrology. 

Apparatus and Measurement Methods at the BIPM 

The laboratory of the BIPM created in 1937 was thus conceived to 
respond to these needs; its equipment can be divided into two entirely 
distinct parts: the electrical facility for providing power to the lamps and 
the specifically photometric installations. 

The direct current electrical supply of the lamps is simple since a rela- 
tive precision of a few parts in 10'' is sufficient; initially assured by lead 
storage batteries of large capacity, the supply is now provided from the 
power lines through the intermediary of rectifiers and stabilizers, giving a 
more versatile operation. 

A single potentiometer permits simultaneous determination of the 
potential difference between the lamp terminals (by the intermediary of a 
voltage divider, however) and the current through the lamp; for the latter, 
one measures the potential difference between the terminals of a 
calibrated resistor connected in series with the lamp (fig. 1). Two lamps can 
be supplied simultaneously on completely independent electrical circuits, 
this was originally required by the measurement techniques used, and 
remains today a practical advantage. 

The photometric measurement of lamps at the BIPM displays a 
characteristic which results from the coordinator role played by the BIPM 
and which greatly facilitates the comparisons; all the lamps to be compared 
are always operated at the same distribution temperature,*' that is to say 
that their radiations have just about the same color; it is therefore not 
necessary, at least in principle, to verify the spectral properties of the de- 
tector, whether it is the human eye or a physical sensor. 

' The terms marked with an asterisk are defined in the lexicon. 



164 




Figure 1. Measurement nf the electrical characteristics nf an incandescent lamp. L. lamp; R. 
calibrated resistor: A. adjustable stabilized supply (direct current); Rli. fine adjustment 
rheostat: T. voltajre divider of total resistance R , and of division ratio p = 0.01: P. measur- 
ing potentiometer: C,. galvanometer. 

a) The reading e, corresponds to the potential difference E between the terminals of L: 



£' = e,/p. oi £=100p, 

{Eh generally between 10 and 200 V.) 

b) The reading e< corresponds to the current / thrcjugh L; 

I=e2lR - EIRj 

(/is generally between 0.2 and 6 .4.) 



Photometric measurement [1] depends on either standards of lu- 
minous intensity* or standards of luminous flux*: thus a difference of only 
a geometric nature separates the two kinds of measurement. Standards of 
intensity are placed directly on a photometric bench in front of the sensor; 
standards of flux are placed in the center of a sphere (fig. 2) provided with 
a small observation window and coated on the interior with a diffusing 
white coating; the window faces the sensor. In the two cases, the measure- 
ment itself is finally the same and consists in attributing a value to the ratio 
of illuminances* received by the sensor in comparing the two standard 
lamps. 

Originally the measurements were visual; the eye can judge correctly 
only the equality of two illuminances, which must therefore be realized 
simultaneously by using an auxiliary comparison lamp; the system for ad- 
justment of the illuminance utilized variation of the distance to the 
photometer, either from the comparison lamp or from the standard lamp 
(fig. 3). Since the spectral sensitivity of the eye is not rigorously identical 
from one individual to another, it was necessary either to have the mea- 
surements made by a large number of persons or to use several observers 
who possessed the "average eye," at the least for a time and under certain 
conditions. This "average eye" has been well defined physically since 



165 




Figure 2. Intc-irating sphere. This device is used for ciimparing standards of lumitKius flux. S. 
sphere (1.5 m diameter): L, standard lamp; L;„ auxiliary lamp: E, opaque screen (15 cm 
diameter): M, spherical mirror: F, observation window (4 cm diameter); R. photoelectric 
sensor: A, area of the interior wall of the sphere, seen by R. via M. E protects F and A from 
direct radiation emitted by L. Tlie illuminance at A is pr(ip<irtional to ihe luminous flux from 
L. 

The interim' wall surface of the sphere carries a coating which should he uniform, stable, 
perfectly diffusing; and with a nonselective high reflection factor. It is difficult to unite 
these diverse properties, but a flat white paint having zinc oxide pigment constitutes a 
satisfactory compromise. 

The lamp L placed at the center of the sphere must be considered as a foreign body 
which "absorbs" a part of its own luminous flux; since this absorption is different from one 
lamp to another, one is led to apply a correction (rarely more than 1%) whose determination 
is provided by L;, (measurements of the flux of L;, with and without L in the sphere). 



166 




Figure 3. Visual comparison oi Inn lamp standards nf himinous intensity. P. visual photome- 
ter: T, comparison lamp (of luminous intensity /): B. pliotometric bench furnished with a 
graduated scale: L|. reference lamp (of known luminous intensity I,): L,, lamp to be 
calibrated (of unknown luminous intensity L,). P and T. movable along B. are rigidly linked 
to each other at the fixed distance (/, which it is not necessary to know. In the course of each 
of the two operations (a) and (b). one displaces the ensemble (P.T) just to the point where 
the eye estimates that there are equal illuminances at P: one then has: 

I,l<h- = II<I- and /,/,/,- = 

whence: 




573-106 O - 75 - 12 



167 



1924, tlianks to an international aJ^reement bearing on the curve of relative 
spectral luminous efficacy V{k) (fig. 4); photometry is then completely freed 
from physiological influence and has thus become a major scientific 
discipline, similar to thermometry for example. Even aside from the fact 
that visual measurements were long and painstaking, their duration 
presented a definite inconvenience because incandescent lamps are stan- 
dards of a slightly peculiar character: they change, as a matter of fact, 
although very slowly, while being used. 



A V{.\) 




' — 1 ■ 1 >- 

400 500 600 700 nm 



Figure 4. Relative spectral luminous efficacy The values adopted by the Commission In- 
ternationale de rEclairaj;e (CLE.) are given in the form of a table [2], at 1 nm wavelength 
intervals from 360 to 830 nm. I {K) is valid for photopic vision (or daytime vision) only; there 
is another curve V'{\) apphcable to scotopic vision (night-time vision). 



168 



A substitute solution was therefore sought; nonsubjective and more 
rapid, and there soon followed the adoption of the selenium photovoltaic 
cell which, under certain conditions of use, constitutes a satisfactory sen- 
sor for photometry. The photovoltaic cell is used in the same way as the 
eye. for determining the equality of two illuminances, the determination of 
the ratio of two standards always resulting from the measurement of 
distances to the sensor. 

A new advance was achieved with the photoelectric cell, today still in 
service. The vacuum cell, of the (/illod-Boutry type (cylindrical anode form- 
ing a Faraday cage around the cathode), presents the enormous advantage 
of excellent linearity, better than 10 for an illuminance ratio between 1 
and 2 for example; this remarkable quality, together with the fact that the 
illuminances to be compared no longer need be realized simultaneously, 
but on the contrary, should be realized successively, has permitted simpli- 
fying the measurement installation (fig. 5). A comparison lamp is no longer 
needed, and the measurement of distances is no longer required; the cur- 
rent given by the cell is proportional to the illuminance on the sensor. A 
potentiometric compensating device, associated with a direct-current am- 
plifier using a null detector, completes the receiver. Although the incan- 
descent lamps to be compared have identical spectral energy distributions 
in principle, it has been judged prudent to correct the spectral sensitivity 
of the cell by means of filters to make it approximately analogous to V(X.) 
thus avoiding a small uncertainty due to the minor differences in spectral 
distribution of the radiation from the lamps. 

This measurement method is rapid, which is beneficial for the stan- 
dard lamps; moreover, it permits total freedom from the law of variation of 
illuminance as a function of distance, a law whose rigorous validity cannot 
be guaranteed (source and receiver of non-negligible dimensions compared 




Figure 5. Photoelectric comparison of two lamp standards of liimincnis intensity. V. double 
opal glass: D,. D2, diaphragms: Oi. O2 objectives: C. cathode of the phuioelectric tube. The 
reference lamp Li (of known luminous intensity I,}, then the lamp to be calibrated L2 (of 
unknown luminous intensity /2) are successively placed at the unknown, but fixed, distance 
d in front of V. D, defines the surface of the cathode which is illuminated and. with D2. the 
geometrical throughput of the beam. The photoelectric current is proportional to /|. which 
implies: 1-1 = I, (kli,) 

169 



to the distance that separates them, atmospheric absorption). It is esti- 
mated that the precision of measurement is better than 0.1 percent, when 
all the precautions in the organization of the measurements, symmetry in 
particular, are taken. 



International Comparisons of Intensity 
and of Luminous Flux 

The BIPM has already utilized its installations five times (1948, 1952, 
1956, 1961, 1969) for comparisons of standard lamps which maintain, in the 
large national laboratories, the two principal photometric units [3]; these 
two units are the candela*, which is either determined directly starting 
with the primary standard at 2045 K (fig. 6), or realized at higher distribu- 
tion temperatures (2357 K and 2859 K), and the lumen* realized at 2357 K 
or at 2793 K (fig. 7). The laboratories participating in these comparisons are 




R(/,) 




L(/) 



R(/;) 



® 



Figure 6. Principle <>{ the calibration of an incandescent lamp hy comparison with the prima- 
ry standard of luminous intensity (2045 K). T. hiackliody (thoria tube): Pt. pure platinum at 
its freezing temperature: Th. thoria powder; C.h. heater: P. prism-lens of transmission fac- 
tor r; A. area (to be determined precisely) oi the aperture of a diaphragm: R. photoelectric 
sensor whose current is prnpoi I ioiial to the received illuminance E,: L, incandescent lamp 
of luminous intensity / to be dctei 
must be constant. 

(a) £, = 600 000(7 -.-i/*/-). from t 



d; </. distance uhii h need not he known, but which 
definition of the candela 



(b) E, = tll(P) 
so that 



1 = 611(1 IWOt ■ A <E-,IE,) 
I = m) OUUt ■ A{i.,ji^) 



170 



in principle those which have reahzed the primary standard, but the mag- 
nitude of the work to be done for this reahzation is such that there are rare- 
ly more than one or two laboratories that have redetermined the candela 
starting with the blackbody before each new comparison. 

The results obtained show some disagreements between laboratories 
of as much as about ±0.8 percent for the candela determined directly from 
the primary standard; this is much larger than the errors (about 0.3%) 
which each laboratory estimates, which proves that there exist important 
systematic errors in the blackbody realization or in the transfer to incan- 
descent standards; studies undertaken on the causes of these errors have 
not yet permitted reducing the differences. 

Under these conditions, it might be feared that the spread among the 
results of the laboratories may be larger for standards of luminous intensity 
at higher distribution temperatures, and for standards of flux; this is happi- 
ly not the case, without doubt by a phenomenon of partial error compensa- 
tion, since the disagreements do not exceed ±1.1 percent (fig. 8). But per- 
haps the most important verification is that in the chain of comparisons 



LUMINOUS 
INTENSITY 



LUMINOUS FLUX 



PRIMARY STANDARD 
(blackbody at the 
freezing point of 
pi atmum) 



SECONDARY 
STANDARDS 
(Incandescent 
lamps) 



2045 K 



Photometer 



2357 K 



J 




2045 K 






blue glass 







Photometer 

i 



Spectrophotometer 



2859-K 



Goni ophotometer 



2357 K 



blue glass 



Integrating sphere 
and photometer 



2793 K 



Figure 7. Crenealngy of photometric' standards. The origin of the various values ot distriliutioii 
temperature attributed to the standards is the following: 2045 K— freezing temperature of 
platinum; 2357 K— temperature obtained by placing a certain blue glass in front of a stan- 
dard at 2045 K; 2793 K- temperature obtaiiic<l !>> placing the same blue glass in front of 
a standard at 2357 K: 2859 K— temperature oi a coioriinetric reference standard. (The ar- 
rows indicate the passage from one standard to the next, with the comparison instrument 
indicated.) 



171 



there has appeared no reduction in the dispersion of the resuhs between 
national laboratories; we have, however, in particular for the comparison 
of 1969, tried to get rid of some defects and uncertainties of incandescent 
lamps by multiplying the precautions taken: choice of a unique lamp type 
only slightly subject to variation during transport, substantial increase in 
the number of lamps in the groups, specification of the manner of excita- 
tion and of the duration of preheating the lamps, etc. If no progress has 
been realized with respect to the dispersion among laboratories, we have, 
however, observed for each laboratory a greater consistency than previ- 
ously between the results of two successive comparisons. 




Figure 8. Results lA' the cdiiiparisou (if national standards of luminous intensity (2045 and 
2859 K) and of luminous flux (2793 K) carried out in 1969. In the three cases, deviation of 
each lahoratory relative to tlir mean. (The abbreviations are those used by the partici|3atin<i 
laboratories.) 



172 



Maintenance of the Units and Stability of the Standard Lamps 



The BIPM maintains reference standards whose values, in candelas 
or in lumens, resuhs from the mean of the groups of lamps sent by the na- 
tional laboratories at the time of the 1952 comparison. These standards are 
used for the varied work carried out at the BIPM and for furnishing calibra- 
tions to laboratories requesting them; several hundred lamps have been 
sent to Sevres since 1952 for calibration or for verification of their calibra- 
tion. The three following international comparisons (1956, 1961, 1969) have 
shown that the reference standards of the BIPM have continually satisfac- 
torily represented the mean of the national standards of the laboratories 
having reahzed the primary standard at least once. 

The uncertainty of the photometric measurements, of the order of 0.5 
percent, is such that an attempt at unification of the national reahzations of 
the candela and lumen, made in 1961, failed; it was finally judged prefera- 
ble to have each laboratory retain the initiative as concerns its own 
representation of the units. This uncertainty is due essentially to the insta- 
bilities of some incandescent lamps; despite a rigorous selection and a 
preliminary aging with the aim of stabiHzing their electrical and photomet- 
ric characteristics, the lamps remain subject, with almost rare exceptions, 
both to a change with time which would be easy to take into account, and 
also, which is more serious, to unexpected variations due to their design or 
to their construction. Some progress has already been made, in particular 
for evacuated lamps usable at a low color temperature (fig. 9); but much 
remains to be done to obtain stable gas-filled lamps, which are, however, 
the most necessary because they are the most used in practice. 

Spectrophotometric Measurements 

The comparison results given above might be interpreted to mean that 
the realizations of the candela and the lumen at different distribution tem- 
peratures are independent units: such is not the case. For example, if the 
photometric laboratories could obtain radiation sensors whose spectral 
sensitivity was exactly proportional to ^''(A.), there would evidently no longer 
be any difficulty in comparing two lamps operated at different distribution 
temperatures. 

There exists, however, a method, which is quite satisfactory theoreti- 
cally for resolving this delicate problem; it consists of dividing the two 
radiations to be compared into a very large number of homologous spectral 
elements and comparing these elements two-by-two, which is a simple 
photometric measurement; the ratio of the two radiations is then obtained 
by taking rigorous account of the values of V{k) in the computation. 



173 





Fi-iure 9. Lamp standard of luminous intensity. Nominal characteristics: 10 V. 5 A. 2045 K, 15 
cd; preheat time 15 min. The type of construction (absence of hooks to support the fila- 
ment), the choice of material (envelope without noticeable defects) and the care taken in as- 
sembling the lamp make it a standard of excellent stability. It must, however, never be for- 
ijotten that an incandescent standard lamp is a fragile instument. particularly sensitive to 
shock and vibration. 



174 



This method of spectrophotometry, rather long but certainly much 
more sure, has already been used several times by the BIPM, to see what 
were the relations which linked the mean representations of the candela at 
2045 K. 2357 K. and 2859 K; the resuhs obtained show that the magnitude 
of the candela is the same in the three cases, to better than about 0.3 per- 
cent, which can be considered as entirely satisfactory in view of the mea- 
surement uncertainties. These results, combined with those of the interna- 
tional comparisons, allow estimating the precision with which the national 
laboratories compare standards of different spectral distribution tempera- 
ture; we note some spreads of 1 to 2 percent which show that the methods 
of heterochromatic photometry used — methods generally based on colored 
glasses — do not offer the hoped-for rehabihty of measurement. In the case 
of the lumen, some older studies lead to similar conclusions. 

International Comparison of 
Distribution Temperature Scales 

We have spoken several times of the distribution temperature without, 
however, completely specifying which scale is involved. For a very long 
time, the BIPM has had available only one scale, rather uncertain but 
nevertheless sufficient for its needs, based on the means of the distribution 
temperatures near 2045 K, 2357 K, and 2793 K, of the national standards of 
luminous intensity and of luminous flux which were involved in the interna- 
tional comparison of 1952. 

In 1963, the organization of the first comparison of standards of dis- 
tribution temperature enabled one to compare the national scales and 
establish a mean scale between 2045 K and 3000 K [4]. The measurements 
made by two different methods, one of which was the spectrophotometric 
method, and at six nominal temperatures distributed rather regularly 
between 2045 and 3000 K, have shown an appreciable spread among 
laboratories from 2600 K up: the maximum spread between the two labora- 
tories whose results are the most divergent reaches several tens of kelvins 
(fig. 10). The resulting mean scale is a practical scale defined at six points; 
despite the disagreements among laboratories, and doubtless here also by 
a happy phenomenon of compensation of errors, one can verify the excel- 
lent coherence of the mean scale to a few kelvins. 

Prospects Offered by Radiometry 

We see that the work of the BIPM has been restricted until now to the 
comparison of incandescent lamps, and it is evident that even aside from 
the reahzation of the blackbody at the freezing point of platinum, there are 
some improvements to be made in heterochromatic photometry and in the 
transfer from standards of luminous intensity to standards of luminous 
flux. 



175 




DAMWi 



Figure 10. Results of the comparison of national standards of distribution temperature car- 
ried out in 1963- 1964. At the six nominal temperatures indicated, deviation of each laborato- 
ry relative to the mean. (The abbreviations are those used by the participating laboratories.) 



But there are also other problems. For example, there exists a dis- 
agreement between the calculated value and various experimental values 
of the maximum luminous spectral efficacy Km^ which is the ratio between 
the luminous flux (in lumens) and the radiant flux (in watts) of a given 
monochromatic radiation at the wavelength 555 nm (maximum of the curve 
V(K)); the calculated value requires a good knowledge of the freezing tem- 
perature of platinum, which has stimulated several national laboratories to 
undertake new determinations of this temperature. Conversely, one could 
also, by convention, assign a value to the luminous efficacy of a given 
monochromatic radiation and realize the photometric quantities by means 
of an absolute heat detector preceded by a V{\.) filter with a known trans- 
mission factor; we would then have a new basis for the candela (or for the 
lumen) which would allow abandoning the blackbody. 

Some studies along this line are underway in several national laborato- 
ries and some encouraging results have already been obtained; neverthe- 
less, an international comparison of incandescent lamps calibrated in 
power units, organized in 1966, exhibited the same dispersion among the 
radiometric scales as among the practical realizations of the candela [5]. 
It would therefore be premature to change the current definition of the can- 
dela. Radiometric measurements, and especially spectroradiometric ones, 
however, open the way to such applications and their rapid development is 
inescapable. 



176 



Small Lexicon of Photometry 



Luminous flux 

Quantity derived from energetic flux (energy transported in the form 
of radiation) by the evaluation of radiation through its action on a selective 
sensor whose spectral sensitivity is defined by the relative spectral lu- 
minous efficacy V(k). 

Unit: lumen, Im 

Luminous intensity {of a source, in a direction). 

Quotient of the luminous flux leaving the source and propagating in an 
element of solid angle containing the direction, by that element of solid an- 
gle. 

Illuminance (at a point of a surface). 

Quotient of luminous flux received by a surface element containing 
the point, by the area of that element. 

Unit: lux, Ix 

Luminance (in a direction, at a point on the surface of a source). 

Quotient of the luminous intensity, in the given direction, of a surface 
element at this point, by the area of the orthogonal projection of that ele- 
ment on a plane perpendicular to the given direction. 

Distribution temperature 

Temperature of the blackbody for which the ordinates of the spectral 
distribution curve of its luminance are proportional, or nearly so, in the 
visible range, to those of the distribution curve of the radiation considered. 

Unit: kelvin, K 

Candela 

SI unit of luminous intensity: the luminous intensity, in the perpen- 
dicular direction, of a surface of 1/600 000 square metre of a blackbody at 
the temperature of freezing platinum under a pressure of 101 325 pascals. 
(13th CGPM, 1967) 

Symbol: cd 

Lumen 

SI unit of luminous flux: the luminous flux emitted per unit sohd angle 
(steradian) by a uniform point source having a luminous intensity of 1 can- 
dela. (9th CGPM, 1948) 

Symbol: Im 



177 



Bibliography 



[1] Walsh. J.-W. T., Photometry, second edition, 532 pages. Constable and Co., London 
(1953). 

[2] Publications of the Commission Internationale de I'Eclairage No. 18, pp. 43-48 (1970), 
and No. 15, pp. 93-102(1971). 

Proces-VerbauxC.l.P.M. 40, Annexe 1. pp. 145-150(1971). 
[3] Terrien, J. and Moreau, H., Rapport sur la deuxieme comparaison des etalons na- 
tionaux d'intensite et de flux lumineux (1950-1952), Proces-Verbaux C.I.P.M., 23-B, 
pp. P76-P100(1952). 

Terrien, J., Moreau, H., and Bonhoure, J., Rapport sur la troisieme comparaison des 
etalons nationaux d'intensite et de flux lumineux (1956-1957), Proces-Verbaux C.I. P.M. 
26-B,pp. P74-P103(1957). 

Bonhoure, J., Rapport sur la quatrieme comparaison des etalons nationaux d'intensite 
et de flux lumineux (1961), Comite Consultatif de Photometrie, 5^ session, pp. 63-87 
(1962). 

Bonhoure, J., Rapport sur la cinquieme comparaison des etalons nationaux d'intensite 
et de flux lumineux (1969), Comite Consultatif de Photometrie, 7'' session, pp. P86-P119 
(1971). 

[4] Bonhoure, J., Rapport sur la premiere comparaison des etalons nationaux de 
temperature de repartition (1963-1964), Comite Consultatif de Photometrie, 6'' session, 
pp. P47-P65(1965). 

[5] Bonhoure, J., Comparaison Internationale des echelles radiometriques. Rev. Gen. 
Electricite, 78, pp. 1001-1007 (1969), and Recueil de Travaux du B.I. P.M. 2, article 20 
(1968-1970). 



178 



CHAPTER IX 



MEASUREMENT OF RADIOACTIVITY 



Generalities on the Methods of Measurement 

The term radioactivity designates the abihty of certain nuc lides to 
emit radiation and particles, and to undergo spontaneous changes. In 
traversing matter, these radiations lose their energy and produce ions.' 
electrons, and photons. The measurement of radioactivity is based on the 
detection of these secondary products; its goal is to determine the average 
number of nuclear transformations (commonly called disintegrations) per 
second, that is to say the activity of a source. 

We can distinguish two classes of detector depending on whether one 
counts the primary particles or photons individually (at least in principle), 
or measures only their average effect. Those of the first class are generally 
called "counters," those of the second can be called detectors. The propor- 
tional counter, which has almost completely supplanted the famous (ieiger- 
Miiller counter, records the passage of a single ionizing particle by multiph- 
cation of the primary ions. It belongs to the first class, just as does the scin- 
tillation counter which consists of, for example, a crystal of sodium iodide 
in conjunction with a photomultiplier which transforms the scintillations 
produced in the crystal by the radiation into electrical impulses, and ampli- 
fies these. In contrast, ionization chambers (integrating type) collect 
without multiplication the charge liberated by the radiation. 

A considerable part of the radiation emitted by a source often escapes 
detection, for example by self-absorption; this prevents a direct measure of 
activity. Some emitters of more than one radiation, however, under certain 
conditions lend themselves to an absolute measurement by the method of 
coincidence counting. An example will be explained in more detail in the 
next section. The results ctbtained are often accurate to a few parts in a 
thousand. 

Let us lecall, in passing, that accuracy refers to the difference 
between the results obtained and the true, but unknown value. On the 



' An ion is an atom or a molecule that is electrically charged. It can be created by the libera- 
tion of one or more electrons from a neutral atom or molecule which lies in the path ot ionizing 
radiation. 



179 



other hand, precision chciracterizes the spread amon<i the resuUs, that is to 
say, their repeatibihty (under conditions as identical as possible) or their 
reproducibility (under varied conditions). The long-term reproducibiHty of 
the results obtained with a well-type ionization chamber can be con- 
siderably better than that obtained from other detectors or assemblies; this 
explains its importance in activity measurements. 

For the BIPM. the principal goal is achieving uniformity of measure- 
ments throughout the world and over a long time. The only sure means is to 
im])rove the accuracy of these measurements; this demands a thorough 
knowledge of extraneous effects which can introduce systematic errors. 
Comparisons of independent measurements carried out in different labora- 
tories not only allows checking uniformity but can also sometimes reveal 
systematic errors. This requires close cooperation with the national labora- 
tories. 

Since the comparison of solid radioactive sources presents several in- 
conveniences—source fragility, mountings not adapted to all detectors, im- 
possibility of simultaneous measurement in different laboratories — it is 
often preferable to compare liquid sources, that is to say, aqueous solutions 
of radioactive salts, provided that these are homogeneous and stable. One 
then measures the activity per unit mass of solution, called radioactive 
concentration. Evidently, this gain in the freedom and generality of the 
measurement introduces new parameters and additional uncertainties aris- 
ing from the determination of the mass of a drop of solution (sampling) and 
the preparation of the sources. These techniques and manipulations must 
be considered as being part of the measurement method. Having deter- 
mined the mass of the aliquot, one can let the solvent evaporate or add it to 
another Hquid (scintillation liquid). 

It is not useful for a small laboratory to try to practice a large number 
of different methods and techniques. In the case of the BIPM. it has 
seemed preferable to choose only two or three methods, to study them, and 
to perfect them as far as possible. The basic method chosen was the 
47r/3(PC)-y method of coincidence counting; this method is generally con- 
sidered as the most accurate for certain radionuchdes. 

The Method of Counting by 47r/3(PC)-y Coincidences 

The BIPM has proposed to study this method in its smallest details to 
increase its precision as much as possible and to consohdate its theoretical 
bases, in order to be able to apply the various necessary corrections with 
more certainty. Long term experiments and special studies on the 
techniques used have already achieved considerable progress. 

The method is applicable to radionuclides which, immediately after a 
P disintegration, undergo a transition with the emission of a photon. 



180 



A source is placed inside a proportional counter (PC) which records 
practically only electrons, irrespective of their direction, and thus has a 
hiiih efficiency (jieometry with a solid angle of 47r sr). A scintillation 
counter using a Nal crystal, placed close to the proportional counter, 
records only the y rays emitted in a limited solid angle, thus has a reduced, 
but constant, efficiency. Now these efficiencies can be considered as the 
probabilities that the corresponding events are recorded. One has to deter- 
mine only one or the other of these probabilities, banking on the simul- 
taneity of the (3 and y events. An appropriate electronic device counts the 
number of coincident events. 

Let us denote by and ey the respective probabilities that disintegra- 
tion ot a source atom will be recorded in the (B channel or the y channel. 
Then the f3-y coim idence will be recorded with the probability e, = e/j • ey, 
since e/j and ey are independent of each other. The counting rate, that is to 
say the number of i)articles. jihotons. or coincidences recorded per unit 
time. pi-j. py. p,.. observed in the three channels, are all proportional to the 
sought-for disintegration rate, Po: 

Pli = poei3, py = poey. 
pr^ Pne,- = pi)eiiey, 

whence 

Pn = Pspylpr. 

Ill this simple formula, we have neglected all loss of counts due, for ex- 
ample, to dead time- or to inevitable delays in the detectors and the elec- 
tronics. It is relatively easy to take account of these effects in an approxi- 
mate way: this seems sufficient in most cases, but there still does not exist 
a rigorous treatment. The work carried out at the BIPM in this fielH is 
described later (p. 188). 

The BIPM has. moreover, always attached much importance to 
technical questions on the counting process and source preparation 
techniques [1.2.3]. Numerous special reports, discussions within Section 
II ol the CCEMRI. and resulting work, address these questions. 

The BIPM Laboratory for Radioniu-lide Measurements 

A 47r/3-y counting system, installed in 1962. comprises several pieces 
of equipment generously donated to the BIPM by various organizations. 
Such a system should always be in working order; it is quickly obsolescent 
and must be updated every 5 years. In addition, a second system was con- 
structed soon after the first, and installed in an air-conditioned room in the 



-The inininuini inUMvul necessary for recordinfi two separate pulses is eaiied detid time (or 
resolution time). To establish well defined conditions, an artificial dead time is often imposed. 



181 



new building oi tlic ioiiiziii^ radiatiims section. Four years later, the elec- 
tronic system was replaced with a c(tmi)letely transistorized system [4]. 
Modifications to ^ive still more cliicicnl actiiiisition of data are in |)rocess. 
Figure 1 gives a view of this setup. 

Our present technicjues for preparing dilutions and sources have been 
taught to numerous foreign guest workers who have come to spend several 
weeks at the BIPM. The manipulations of source preparation are illus- 
trated by figure 2. 

Let us recall finally that the BIPM has prepared and standardized 
nearly 10 000 sources since 1963; several hundred of these have been 
placed at the disposal of various national lalxiratories. 




Figure 1. \ ii-u 111 llic LilI'M syslciii lor' i'(iuiitin;i liy llic \-Trlj^\'(.)-y ('iiiiicidence method. A: 
lead castle eoiitaiiiin^ the dctectois and the sduicc to lie measured: B: bottle eontainiii}; 
fias which circulates tliiciii;ih the iiroportional i-ouuter; C: preamplitier ot the scintillation 
counter (for y radiation); U: transistorized elect i onic system; E: counter displays: F: 
electronic tiniei' and printer; (i: oscilloscope (1(0 various checks): H: hi.uh-voltaiie supply 
lor the detcctoi s; I: nuiltichannel analyzer (for recordint; y specti a). 



182 




d e f 

Figure 2. Preparation of radioactive sources. Manipulations are carried out with gloves to 
avoid contaminating the hands, a: The polyethylene pycnometer containing radioactive 
solution; the end seal of the drawn-out neck is being cut. b: First weighing of the pycnome- 
ter on the platform of a microbalance. The pycnometer ( = 1 g) contains 1 to 2 gof solution, 
c: Deposition of several drops (50 mg. on the average) on the support. This latter is a film of 
thin plastic. metalHzed and stretched across the hole of a metallic washer, d: Second 
weighing of the pycnometer; the mass of solution used is obtained by the difference from 
the preceding weighing, e: A drop of wetting agent is added to each source with the aid of 
another pycnometer. f: Drying the sources in a current of air. The cleanliness of the instru- 
ments must be carefully guarded. 



Radioactivity Standards 

More than 1800 nuclides are known today; most of these are radioac- 
tive. The measured half-lives^ range from less than a microsecond to more 
than a biUion years. The radionuclides of metrological interest have half- 
lives between an hour and several thousand years. For the choice of a stan- 
dard, it is important to recall that the results of a measurement of radioac- 
tive decay of, in general, a mixture of radionuclides depend on the values 
of the half-lives of each radionuclide present, and on the mixture ratios of 
the radionuclides. These ratios are not known with certitude; the useful life 
of a standard is therefore also not known. A practical solution consists of 
preparing a batch of standards and replacing it with a new batch well be- 
fore the sources become too weak. 

In principle, the unit of activity could be maintained with the help of 
a single absolute measurement device, without use of standard sources. It 
has been estabhshed, however, that a 47r)8(PC)-y system, probably the 
device best adapted to this use, can remain unchanged for only a few years. 

^The radioactive half-life is the time required for the activity to decrease to half its initial 
value. 

573-106 O - 75 - 13 



It is therefore safer to refer also, if possible, to one or more appropriate 
standard sources. At the BIPM we have chosen a certain number of "^"Co 
and "^^Mn sources, havin"; respective half-lives of 1926 and 312 days; in the 
course of measurements, we slip these in among the sources whose activity 
is to be determined. Each standard can be used for one or two half-lives 
and then must be replaced by a new source. This procedure guarantees 
good continuity of measurements while furnishing absolute results. It has 
the inconvenience of being valid only for the radionuclides mentioned and 
requires a rather delicate source preparation. 

In certain cases, we prefer to sacrifice the absolute character of the 
method, and thus the measurement accuracy, for the benefit of better 
precision. This is the case for current-measuring ionization chambers like 
the well chamber (where one has provided a tube, or well, for placing the 
source inside the chamber). Such a chamber, also called a 47ry chamber, 
can constitute a reference device of very high reliability for y emitting 
radionuclides if the current measurements are made relative to an ap- 
propriate radium source (half-life ~ 1600 years). 

The BIPM has embarked on a permanent reference system for inter- 
national comparisons. This system comprises a 4<TTy chamber, an automatic 
system for current measurement, and a set of special radium sources. 

It is expected that the national laboratories that distribute radioactive 
solutions will send some of their production ampoules to the BIPM. We 
shall measure them, store them, and communicate the complete results, 
thus establishing the possibility of relating these standards and achieving 
uniformity of activity measurements on y emitters. 

The international radium standard, stored at the BIPM (see p. 37). no 
longer has great metrological importance aside from its historical interest 
and its well defined mass of very pure radium. The mobility of the salt in its 
container diminishes the vaUdity of ionization measurements, and the in- 
creasing fragility of the container forbids frequent use. 

International Comparisons of Radionuclides 

We estimate that we can measure the activity of certain radionuclide 
sources, such as *'"Co, to a few parts in a thousand. This uncertainty is com- 
posed of a random part and a systematic part. The first can be determined 
by the laws of statistics: it decreases when the number of independent 
measurements increases. The second, however, is determined only by an 
estimate whose validity depends on the experience of the operator and the 
extent of possible variations of parameters (method, operator, laboratory, 
measurement conditions, etc.). 

The systematic error can be estimated on firm grounds only if com- 
parative measurements are carried out between various laboratories and 
by different methods. The CCEMRI has recognized this need since the 



184 



beginnin<i; of its existence. Numerous comparisons of radionuclides had al- 
ready been made before, but it was considered desirable that they be con- 
tinued on a more extensive and official basis. The goal, which might seem 
ambitious, was formulated by the CCEMRI in 1961: "It is desirable that an 
accuracy of ±1% — possibly going to ±0.1% in certain cases — be attained 
in the standardization of radionucUdes." 

Comparisons organized by the BIPM began in 1961 at a very rapid 
pace but this subsequently slowed down (see table 1). As each of these 
comparisons has been described in detail [5], we limit ourselves to 
presenting here some interesting figures. 

Part of the results of the international comparison of ""Co in March 
1963 is represented graphically in figure 3. One will note the small dif- 
ference (statistically significant) linked to the method of weighing drops of 
solution. Several authors have subsequently very carefully studied this dif- 
ference which would have perhaps passed unnoticed if the comparison had 
not revealed it. 

The temporary halt of comparisons after 1967 was due to the predomi- 
nant opinion of the participants who found that the results, often difficult 
to interpret, did not always justify the difficult work since a certain number 
of problems had not been studied [6]. These problems have been dis- 
tributed among several working groups of which one is rightly charged with 
preparing new proposals for international comparisons. 

Statistics of Counting 

All the tasks undertaken in this field at the BIPM have their origin in 
a practical goal. In certain cases, it is a matter of finding, adapting, or 
developing methods which permit the extraction of maximum useful infor- 
mation from the results of measurements which have been made with the 
greatest possible care. In other cases, one is led to the use of statistical 
reasoning to more correctly describe an observed process, as, for example, 
the counting of pulses of nuclear origin whose distribution departs ap- 
preciably from a simple Poisson Law.^ To neglect these deviations or to 
take account of them only in an imperfect way would inevitably introduce 
systematic errors. Finally, such a description can sometimes give rise to a 
new measurement method. 

Here are some examples of applications in different fields which have 
been treated at the BIPM: 

- Exploration of experimental data: analysis permitting discovery 
of distortions due to a dead time, method of extrapolation of the 
profile of a spectral line of a particles to zero intensity, smoothing an 
experimental spectrum. 

^ In this case, the probabihty of observiii}; n pulses in a time interval / is given hy e-"' (pt)" jn\. 
where p is the counting rate (mean number of pulses per unit time). 



185 



AAEC 

BCMN 

CENS 

IKO 

IMM 

ISS 

JEN 

PTB 



( 1 

c 



I I 



AECL 
AIEA 
BIPM 

CNAM 
ETL 
ISN 
NBS 
NPL 
NPRL 

NRC I I 

UVVVR I 



c 



0,1% 



-I — I — I — I — 1 — I — I — I — r 

1510 



-I — I — I — I — I — I — I — I — I — 1 — 1 — I — I — I — I — I — |- 



1520 



1530 s-''mg-'' 



Figure 3. International comparison of a solution of ""Co (May 1963). The horizontal bars 
represent mean results (activity per gram) with their standard deviations. The vertical lines 
(broken) indicate arithmetic means of groups of results obtained either by the pycnometer 
method (P). or by the ""extrapolation" method lE) in which the deposited drops are weighed 
directly, but in which aUowance must be made for evaporation before and during the 
weighing, by extrapolation to the initial instant. The initials at the left designate the par- 
ticipating laboratories. 



186 



Table 1. Resume of ihe eleven inteiiiatioiial eoniparisons 
of radionuclides orjranized !)) the BIPM 











Number of 


Range of 






Number of 


Total 


selected 


tfie selected 


Radionuclide 


Date 


participants 


range 


results 


results 








(%) 




(%) 


32p 


Jan. 1961 


16 


6.0 


13 


2.0 


131| 


April 1961 


16 


4,0 


12 


1 .5 




Jan. 1962 


25 


3.1 


15 


2.5 




Jan. 1 962 


21 


9.0 


18 


3.0 


204TI 


May 1 962 


19 


14 


14 


5.9 


355 


June 1962 


15 


18 


4 


6.5 




March 1 963 


22 


4.6 


19 


1.4 


"'Am 


June 1963 


21 


3.1 


13 


0.8 


™(Sr + Y) 


Feb. 1964 


23 


3.0 


16 


2.0 


"Mn 


Apr. 1965 


16 


14 


15 


6.0 


^°Co 


May 1967 


24 


1.7 


20 


0.9 



— Process description: superposition of regenerative processes,^ 
time intervals between pulses after an extendable dead time (fig. 4), 
modifications of a Poisson process by a nonextendable dead time, 
effect of two successive dead times, statistics of pairs of pulses, 
time intervals between correlated pulses. 

— New methods: determination of dead time to better than 0.1 per- 
cent, coincidence counting by a delay method, measurement of 
secondary pulses. 

Most of the problems concerning dead time have been described in 
two articles which give a comprehensive view of the current state of our 
knowledge in this area [7,8]. Other studies have been treated in internal 
reports of the BIPM; these are available on request. 

The majority of these studies aim at a better knowledge of the cor- 
rections to be applied to counts obtained by the 47r/3-y method. The study 
of perturbations capable of causing systematic errors is a permanent task. 
Numerous problems are not yet resolved in a satisfactory way, as, for ex- 
ample, the loss of coincidences produced by the dead times in the /3 and y 
channels. At the same time, these already well-advanced studies are being 
actively pursued, with the aim of a simplified apphcation of the correlation 
method. This method is a new route which may rival the direct measure- 
ment of coincidences. 

To illustrate the results obtained by these studies, we have chosen the 
two following examples which outline some new measurement methods 
that have already aroused hvely interest in other laboratories. 

^In a regenerative process, successive events occur independently of each other. Such a 
process is thus completely characterized by the distribution function of the time intervals 
between successive events. 



573-106 O - 75 - 14 



187 



original series 



I — I H 1 



t 



after a non-extendable 
dead time 



after an extendable 
dead time 



t 



Figure 4. Effect of dead time on a series of pulses. For a nonextendable dead time, each 
recorded pulse is followed by a dead time of duration r which prevents counting pulses 
which may arrive during this interval. In contrast, for an extendable dead time, all pulses, 
recorded or not, are followed by a dead time of duration r. The times of insensitivity. dif- 
ferent according to the type of dead time, are indicated by the hatched rectangles. 



superposition 




deed 






time 








T 






Figure 5. Precise measurement of an imposed dead time. 

— upper: scheme of the principle for measuring t with the use of two oscillators. 

— lower: counting rate r measured as a function of the frequency i^i; v-i\v\ is assumed 
constant. 



a) Precise measurement of dead time 

If the elaboration of more and more rigorous correction formulas for 
lost counts is indispensable, it is important that the numerical values in- 
serted into these formulas be sufficiently accurate, in particular the dura- 
tion of the dead time. Traditional techniques (two-source method, decay 
method) all have the inconvenience of being tedious and of low precision. 
Furthermore, they assume that the original process follows a Poisson Law 
strictly and that the type of dead time is known in advance. Now to mea- 
sure a dead time, we are not obliged to use a series of pulses coming from 
a natural source; it is only important to know the distribution of time inter- 
vals between successive events. This distribution is particularly simple if 
we use a superposition of pulses coming from two oscillators of frequencies 
and v-z (with V\ > p-t)- Figure 5 illustrates the results obtained for the 



188 



counting rate r of the superposed process. It is assumed that the length of 
the pulse is neghgible with respect to the dead time t. For the range Vi < 
1/2t. r is independent of the type of dead time, t can be deduced from the 
relation 

T= (l^i + V2 — r)l2viV2. 

On the other hand, for Vi > 1/2t, the counting rate r depends on the type of 
dead time and thus permits its identification. 

b) Measurement of secondary pulses 

Questions concerning the detection of secondary pulses hold a par- 
ticular interest for all absolute measurements of activity, for the occasional 
occurrence of more than one pulse for a single initial event risks a syste- 
matic falsification of the count. Such duphcations can show up by their in- 
fluence on the distribution of intervals between successive pulses. Other 
perturbations of the process under study have, however, a similar effect, 
and if an anomaly is observed it is often difficult to attribute it to the 
phenomenon of double-pulsing with certainty. For a series of pulses con- 
taining simple events which occur individually and thus which appear in 
the form of pairs, the total number of observed counts per time interval t can 
be decomposed into k = ki + 2k2, where ki and k2 are respectively the 
number of simple pulses and the number of pairs in t. We note that k and 
ki are both even or both odd, whatever is. Analogously we can write for 
the total counting rate, p'"' = pi + 2p2. This property is the basis of a 
statistical method which allows resolution of the contributions pi and p2 to 
the total counting rate. 

The pulses are directed to an electronic flip-flop which changes state 
each time a pulse arrives; the same pulses are also sent to a second flip- 
flop, but after a delay t during which k pulses reach the first flip-flop. Each 
flip-flop controls a gate which opens and closes alternatively after each 
pulse. The two gates are initially in the same state: they find themselves 
again in the same state if k is even and in different states if k is odd. Ex- 
amination of the state of these gates allows determination of the probabili- 
ties Prob {k even) and Prob {k odd). We also know how to calculate these 
probabilities in the case where the distribution of separation follows a Pois- 
son law; the probably that k is odd is independent of the number of pairs of 
pulses and is given by 

Prob odd) = 1/2 [l-exp(-27rif)]. 

Since Prob {k odd) is measured, this relation allows the computation of pi. 
Moreover, one obtains ptot by direct counting, and calculates 

p2 = l/2 (ptot - Pi). 

If the delay t is much less than the mean interval 8 between the pulses 
forming a pair, only a single one of the two pulses of a pair can appear in 



189 



this interval, in general. On the contrary, if t is much larger than 8, the two 
pulses of a pair practically always appear in the same interval. Figure 6 
shows that these limiting behaviors are independent of the distribution of 
the interval between pulses of a pair. 

This reasoning has been fully confirmed by experiment. Even for a 
ratio so small that p2/ptot~ 0.005, the secondary pulses show up clearly and 
can still be measured. 

Some details on this new type of measurement and a generalization of 
the method in the case of multiple secondary pulses are found in the 
references [9-11]. 




8 

Figure 6. Measurement of secondary pulses. Graphical representation of — In R(t), where 
R(t)= 1—2 Prob (A- odd), for a distribution which is originally Poisson. The two straight 
hnes represent the behavior limits; the difference of their slopes is proportional to the 
counting rate p-y of paired pulses. The intervals between pulses of a pair are assumed equal 
to 6 (case A) or distributed about the mean value 5 according to an experimental law (case 
B). 

Energy Measurement: Alpha-Particle Spectrometry 

In 1965, it was decided that the BIPM would engage in the field of 
energy measurement of a, j8, and y rays to be able to express an official 
opinion on the energy of certain lines. It was first occupied with a 
spectrometry, where the need for unification was urgent and where it could 
benefit from certain previous experience. 

Nearly 300 a-emitting radionuclides are known; this is slightly greater 
than the number of stable nuclides. The a particle is a helium nucleus with 
electric charge +2e, comprising two protons and two neutrons. For each a 
emitter these particles are ejected with one or more discrete energy values. 
The excellent definition of these energies, normally between 4 and 9 MeV, 
gives them the quality of standards. 



190 



The preferred method for measuring absolute energy is that of deflec- 
tion by a uniform magnetic field. Knowing that a charged point mass having 
a velocity perpendicular to the direction of the field describes a perfect 
circle in vacuo, one measures the magnetic flux density B and the radius 
r of this circle. The kinetic enrgy Ea is then, except for a relativistic 
correction, 

Ea=i2elm)iBr)\ 

where 2e and m are respectively the charge and mass of the a particle. 

The magnetic spectrograph of the BIPM (fig. 7) is the only one in the 
world which has been specially designed for the absolute measurement of 
the energy of a particles. The electromagnet of 8.5 Mg has a semicircular 
airgap of 650 mm radius and 70 mm spacing. The flux density, stabilized to 
about 1.5 X 10^^ with the help of a proton-resonance probe, can have 
several values between 0.6 and 1.0 T. Into the spacious vacuum chamber, 
one places either the device for measuring magnetic flux density, or the 
spectrograph proper; this latter essentially comprises a slit and a photo- 
graphic plate held in the same plane at a fixed distance apart by a rigid bar. 
The photographic plate serves as an a-particle detector. The principle of 
the functioning of the semicircular spectrograph is indicated in figure 8. 




Figure 7. Overall view of the BIPM magnetic spectrograph lor absolute measurement of the 
energy of a particles. A: electromagnet (mass 8.5 Mg), maximum flux density 1 T; B; 
water-cooled coils; C: cover of the vacuum chamber; D: device for stabilizing the mag- 
netic field using proton resonance; E: turbomolecular vacuum pump (speed: 900 m^ h^'). 



191 



Figure 8. Diagram showing the principle of the semicircular spectrograph. Under the action 
of the uniform magnetic field perpendicular to the plane of the figure, a particles of the 
same energy follow circular paths of the same radius r. A: pole face of the electromagnet; 
B: a-particle source; C: slit; D,D': a-particle paths; the particles emitted perpendicularly 
to the direction CF (path D) give the limit of the recorded line; E: rigid bar to maintain the 
distance from C to G; F: detector (photographic plate); G: reference scale whose distance 
from C has been previously measured. The scale is recorded on the photographic plate at 
the same time as the a-particles. 

The distance between the sUt and the detector impact point of the par- 
ticle emitted by the source depends upon the energy of the particle and on 
its direction of passage through the slit. To a group of monoenergetic parti- 
cles emitted by a source of limited size, there corresponds a calculable dis- 
tribution of surface density of the number of particles on the detector (fig. 
9). Since sources are not infinitely thin, the energy of a group of particles 
spreads, because of self-absorption, over a certain range which is called a 
"line"; its upper hmit does not depend on the source thickness. This limit 
can be determined by extrapolating to zero the density of tracks on the 
plate. Experience confirms that this density increases as the 3/2 power of 
the distance from the extrapolated point. Consequently, if the density is 
plotted to the 2/3 power on a graph, the observed values lie on a straight 
line, except for statistical uncertainties. By extending this hue to its inter- 
section with the baseline (fig. 10), one obtains the extrapolated point whose 
distance from the inner edge of the sht is equal to the diameter 2r. The 
baseline, always present, comprises tracks whose origin is not in the 
source. Details of the method and of the experimental device are described 
in the reference [12]. 

At the time of writing, 37 different lines from 24 emitters have been 
measured with uncertainties varying between 10~^ and 10"'*. These new 
results have permitted adjusting a large number of earUer measurements 
and publishing a complete catalog of recommended a-particle energy 
values [13]. It must be noted, moreover, that starting from the energy of an 



192 



a particle and recoil nucleus, one can calculate the energy of disintegration 
which, in turn, is equivalent to the difference between the mass of the 
emitting atom and the sum of masses of the residual atom and the a 
particle. The systematics of atomic masses makes large use of the new 
values of a-particle energies determined at the BIPM. 

Despite the limited number of a emitters which can be measured, 
these experiments are far from being finished. Problems relating to the 
state of the sources and to the natural widths of the lines have not yet really 
been touched, but will merit special attention. 




Distance (in mm) from the extrapolated point 

Figure 9. Line profiles obtained by semicircular spectrography. The a-particle tracks have 
been counted in 0.02 X 5 mm bands on the photographic plate as a function of distance from 
the slit (fig. 8). A measured profile, thick source; O measured profile, thin source; - profile 
calculated for monoenergetic a particles. 



193 



N 



4 



y. 



IS 



10 



129.00 12«,10 

Position on plate {mm) 



V/ 



\ 



1 keV 



I 



Ba s 



1 



1 



128.00 12fl10 

Positron on plate (mm) 



Figure 10. Edge of an a-particle line; at the left the distribution of A', at the right that of N^'^; 
N: number of tracks counted (and statistical uncertainty) per band of 10 /Ltm width. The ab- 
scissa indicates the position on the ph(jtograpliic plate; the particle energy increases to the 
right. The extrapolated point, marked by an arrow, is the furthest point the particles reach. 



194 



Bibliography 

[1] Rytz, A., Standardization of *'"Sr+ '"'Y by means of a chemical separation, in "Stan- 
dardization of Radionuclides," IAEA, Vienna, pp. 247-256 (1967), and Recueil de 
Travaux du B.I.P.M. 1 , (1966-1967). 

[2] Rytz, A., Colas, C, and Veyradier, C, Some experiments on the dilution of radioactive 
solutions and the uniformity of mixing, Recueil de Travaux du B.I.P.M. 2, article 25, 8 
pages (1968-1970). 

[3] Colas, C. and Rytz, A., La resistance electrique des supports et des sources utilises 
dans le comptage 477/3-7, Recueil de Travaux du B.I.P.M. 3, article 18, 8 pages (1971- 
1972). 

[4] Description of assembly No. 3 for counting by 47r/3(PC)--y coincidences. Rapport BIPM- 
75/2. 

[5] See. for example, the appendices to CCEMRI, 4th session. 1963, and 5th session, 1964. 
[6] CCEMRI, Section II, 1st meeting, p. R17 (1970). 

[7] MiUler, J. W.. Dead-time problems, Nucl. Instr. and Meth. 112, pp.47-57 (1973), and 

Recueil de Travaux du B.I.P.M. 4, article 20 (1973-1974). 
[8] Miiller, J. W., Some formulae for a dead-time-distorted Poisson process, Nucl. Instr. and 

Meth. 1 1 7, pp. 401-404 (1974). and Recueil de Travaux du B.I.P.M. 4, article 21 (1973- 

1974). 

[9] Miiller, J. W., Some notes on pair statistics, Recueil de Travaux du B.I.P.M. 4, article 

24, 12 pages (1973-1974). 
[10] Miiller, J. W., A new method for distinguishing between pairs and single pulses, Recueil 

de Travaux du B.I.P.M. 4, article 25, 10 pages (1973-1974). 
[11] Miiller, J. W., A complex modulo K counter, Recueil de Travaux du B.I.P.M. 4, article 

26, 16 pages (1973-1974). 
[12] Grennberg, B. and Rytz, A., Absolute measurements of a-ray energies, Metrologia 7, 

pp. 65-77 (1971), and Recueil de Travaux du B.I.P.M. 3, article 26 (1971-1972). 
[13] Rytz, A., Catalogue of recommended alpha-energy and intensity values. Atomic Data 

and Nuclear Data Tables 12, pp. 479-498 (1973), and Recueil de Travaux du B.I.P.M. 

4, article 31 (1973-1974). 



195 



ii 




CHAPTER X 



X AND GAMMA RAYS 



Generalities 

The Quantity ''Exposure.'' The Principle of the Ionization Chamber With 
"Air Walls." 

Ionizing radiations are frequently used to produce modifications in 
matter— modifications sometimes physical (tests of materials for nuclear 
reactors), sometimes chemical (polymerization of plastics), sometimes 
biological (treatment of cancer). These radiations must be measured and 
checked at the time of use. In situations of this kind, the radiation is con- 
sidered not from the point of view of the source producing it, but from that 
of the material which is irradiated: whence the name dosimetry (literally, 
measurement of dose) given to the measurement of quantities which 
characterize radiations of this kind. 

As to X and y radiations, one uses a particular modification of matter 
which lends itself well to measurement: the ionization of air. Photon radia- 
tions are not directly ionizing: in the first step, the photons liberate fast 
electrons,^ these then progressively lose the energy which the photons have 
given them, by exciting and ionizing atoms in their path. When photons 
liberate electrons in a small volume dF, the resulting ions appear in the en- 
tire neighboring region. This zone of influence has dimensions which vary 
with the energy of the radiation, from about a millimetre to several tens of 
centimetres in air, depending on whether it is a matter of hard or soft x 
rays. 

Whatever be their initial kinetic energy, the electrons practically al- 
ways expend the same energy on the average in producing a pair of ions in 
a given medium. This energy, customarily designated by the symbol W, is 
about 54 X 10^'^ J in air. The number of ions obtained is thus proportional 
to the energy transferred by the photons to the electrons and allows charac- 
terization of the beam of photons. This is why one defines at a point M of a 

' In the field of interest to us, two processes are responsible for the production of electrons: 
the photoelectric effect in which the photon loses aD its energy in expelling an electron from an 
atom, and the Compton effect, an elastic collision with a free electron in which the electron 
receives and carries away part of the energy of the incident photon, the remainder appearing 
in the form of a scattered photon. 



197 



eH 




F 



Figure 1. Principle of the air-wall ionization chamber. A: beam of x rays: B: collector plate 
(potential ~ 0); C: grounded guard plate (potential 0); D: plate at a potential of a few 
kilovolts, the electric field of about 20 000 V • m~' thus created between D and B-C allows 
coUection of the ions; E: region of length / (several centimetres) from which are collected 
the ions reaching electrode B, the charge which they transport is measured by the device F. 
A few examples of electron paths are shown, only the ions produced on the portion of the 
paths shown in heavy lines are collected. The upper part of the figure illustrates a typical 
case of compensation; the three trajectory portions utilized are on the whole equivalent to 
the trajectory T. 

beam of x or y radiation a quantity called exposure,^ derived from the elec- 
tric charge carried by the ions produced in air by the electrons liberated by 
the photons in the mass of air Am contained in a small volume surrounding 
the point M. 

The diagram of the air-wall ionization chamber shown in figure 1 in- 
dicates the principle of the measurement of exposure. Between two parallel 
plates, there is an electric field which can collect the ions produced by the 
pencil of x rays passing through the center of the chamber. According to 
the above, determination of the exposure at the point M in the diaphragm 
aperture requires measuring the total ionization produced by the electrons 
which come from the small volume AV surrounding M, and this ionization 

^ The definition of exposure given by the International Commission on Radiation Units and 
Measurement (ICRU). Its latest formulation (1971) is as follows: "The exposure X is the quo- 
tient of dQ by dm, where dQ is the absolute value of the total charge of ions of one sign 
produced in air when all the electrons (negative and positive) liberated in a volume element of 
air of mass dm are completely stopped in air. The special unit of exposure is the rontgen (R). 
I R = 2.58xlO-''C kg-i." 



198 



only. This is evidently impossible, for inside the chamber, the ions which 
interest us are inextricably mixed with those generated by electrons 
liberated along the path of the photon beam. But thanks to compensations 
like that indicated in figure 1, the charge Q collected from the central re- 
gion of the chamber provides the desired information and consequently the 
exposure at M.^ 

This impUes that the cross-hatched volume in the figure is surrounded 
on all sides by a sufficient thickness of air (hence the name "air-wall" 
chamber): in fact, if the diaphragm is too close to the hatched volume, the 
compensation will be only partial, also, if the two parallel plates are not suf- 
ficiently separated, some electrons will strike these plates and their paths 
will thus not be totally utilized for the production of ions in the air. 



The Concept of a Standard of Exposure 

It would seem natural to choose as a standard, the exposure at a 
designated point in a reference beam. But the definition of such a beam 
cannot be envisaged for x rays because an x-ray tube emits complex radia- 
tion which is known only imperfectly. In the most favorable case of y 
radiation emitted by a radioactive source, stability of the beam imphes that 
the geometry of the system (and also that of nearby objects which could be 
sources of scattered radiation) remains fixed. 

By reason of these difficulties, the unit of exposure is not maintained 
by the use of a radiation beam. The role of standard is assigned to the in- 
strument for measuring exposure: an ionization chamber can constitute a 
standard of exposure rate,^ since it permits determination of this quantity 
from the measurement of two base quantities: electric current and mass.^ 
But it is impossible to experimentally reproduce the ideal situation as- 
sumed in the definition of exposure: the measurement of this quantity can 
be made only indirectly, thanks, in particular, to the compensations in- 
dicated earlier. Whatever standard chamber is used, it is necessary to 



^ If the beam is parallel (and if we neglect the attenuation of photons associated with the 
liberation of electrons), the exposure at M would be the quotient of Q by the mass of air con- 
tained in the cross-hatched volume. In reality, the beam diverges, but (always if we neglect 
the attenuation of the photons) there are as many photons coming through the aperture as 
through successive sections of the beam perpendicular to the axis, only the area in which they 
are distributed being changed. Similarly, the production of electrons remains constant in the 
slabs of air successively traversed by the beam. From this it can be deduced that the exposure 
at M is equal, in the first approximation, to Q/Alp, where A is the area of the aperture, / the 
length of the collection region, and p the mass density of the air (see [1] for a more complete 
analysis). 

* Exposure rate = exposure/time 

^ In fact, these two quantities are measured in an indirect way: this has been indicated above 
for the mass of ionized air (= ^ Ip), we shall see it later for the ionization current. 



199 



determine various correction factors which allow, starting with experimen- 
tal results, calculation of the value of exposure at a given point in the beam 
which conforms to the ideal conditions of the definition. Finally it is the un- 
certainty in the determination of these factors which hmits the accuracy of 
measurements of exposure. 

Measurement of X Radiation 

Measurements of Exposure at the BIPM 

Since the beginning of work in this field at the BIPM (1962), we have 
tried to obtain good measurement conditions, which presupposes a highly 
stable radiation emission. In an x-ray tube, the x rays are produced by the 
impact of an electron beam on a tungsten target. The radiation emitted wiU 
be stable if the number and energy of the electrons striking the target are 
both constant, which imphes simultaneous stabilization of the tube current 
and the appHed high potential (5 to 150 kV and 100 to 300 kV for the BIPM 
tubes). This potential is supplied by an electrostatic generator; by adding 
a supplementary regulating device, we have reduced its already small fluc- 
tuations to a few parts in a hundred thousand. With respect to the current, 
instead of adjusting the filament heating directly, we have done it more 
closely by using an error signal from the fluctuations of tube current. In 
this way it is possible to achieve a stability in the neighborhood of a ten- 
thousandth. 

Figure 2 shows the 150-kV x-ray tube and the BIPM air-wall ionization 
chambers. The quantity usually determined is the exposure rate. It is 
therefore necessary to measure the ionization current resulting from the 
collection of ions. This current is very small, of the order of a few picoam- 
peres or a few tens of picoamperes. It is measured by the Townsend 
method: the ionization current charges a capacitor of capacitance C; the 
potential difference AU, proportional to the time of irradiation At, appears 
across the terminals. The measurement consists of determining the time At 
which corresponds to collection of the charge CAU. With the aid of a device 
developed and constructed at the BIPM since 1963, we have achieved a 
precision of the order of a ten-thousandth in the measurement of these very 
small currents. This precision allows us to carry out studies of phenomena 
(see below) causing small variations of the ionization. 

It has been stated much earlier that to obtain the exposure, various 
correction factors must be applied to the results of ionization measure- 
ments: it is necessary, for example, to take account of the attenuation of 
the photons by the air in the chamber, of the parasitic ionization due to 
scattered photons, etc. The BIPM has worked on improving the accuracy 
of the determination of these factors on which the measurement of expo- 
sure depends strongly. Thus the attenuation by air is measured by placing 



200 




Figure 2. Measurement of exposure in a beam of x rays. A: x-ray tube (capable of being 
oriented so that either of the chambers B and C can be irradiated); B: standard chamber 
for soft X rays (plate spacing 7 cm, collector potential 1500 V); C: standard chamber for x 
rays of intermediate energy (plate spacing 18 cm, collector potential 4000 V). 



an evacuated pipe between the tube and the chamber. Studies on two of 
these factors have been pubhshed. One of them [2] concerns the recom- 
bination of ions, a phenomenon which depends upon the appHed electric 
field. Whatever field is used for the measurements, the collection of ions is 
incomplete (99.8 to 99.9% under usual conditions) and an extrapolation of 
the results to an infinite field is necessary. We have succeeded in deter- 
mining experimentally the part which should be attributed to each of two 
types of recombination (initial recombination and volume recombination); 
this permits making a valid extrapolation for obtaining the saturation cur- 
rent. 

Another experimental study has been devoted to the influence of 
water vapor on the ionization produced in an air-wall chamber [3]. An air- 
wall chamber was placed in an airtight tank. A closed circuit connected to 
this tank comprised a pump producing gas circulation by compressing a 
flexible tube, a drying or humidifying device, and a dew-point hygrometer. 
Drying was obtained by use of a trap immersed in a mixture of methanol 
and dry ice; in this way no chemically foreign substance could pollute the 
air used in the chamber. If one takes account of the effect of water vapor on 
a) the liberation of electrons by photons, or b) the ionization produced by 
the electrons, and if one assumes that in these two cases the air and water 



201 



vapor play entirely independent roles, a linear variation of ionization cur- 
rent as a function of water vapor content is predicted. The experimental 
results are very different from these predictions in the range of low humidi- 
ty. Since the hypothesis of independent roles is very questionable as con- 
cerns b), the observed disagreement can be interpreted as due to a non- 
linear variation of mean energy fV needed to produce a pair of ions, as a 
function of the proportion of water vapor contained in the air (fig. 3). 



1 


^ ^humid air 












^dry air 

10 20 


30 


40 


50 


Relative humidity at 21 °C 

60 70 80 90 
1 1 1 1 *^ 


0,998 
0,996 


o\ft) 








~~ ' ~" — " — — A_ 


0,994 
0,992 










' ~ ___o ° o 

B 



Figure 3. Variations of the mean energy P'^ necessary for production of a pair of ions in air as 
a function of relative humidity. 

Curve A corresponds to theoretical predictions, curve B is derived from experimental 
results. 



International Comparisons of Exposure Standards 

Direct international comparisons have been made at the BIPM since 
1966 for several qualities of soft x rays (10-50 kV) between the standard 
chamber of the BIPM and some national exposure standards (United States 
of America, Canada, Netherlands, Sweden, Hungary) [4]. The differences 
(0.5% at the most) are generally compatible with the estimated uncertain- 
ties. We have nevertheless observed systematic differences between stan- 
dards of small dimensions (4-cm plate separation) and standards of larger 
dimensions (plate separations of 6 to 12 cm) (fig. 4). This can be attributed 
to inaccurate corrections for the small standards, notably the correction for 
scattered photons (at 10 kV) and that for insufficient plate separation (at 50 
kV)." The tracking down of systematic errors is one of the interests in this 
type of comparison and the principal preoccupation of the BIPM. 



•'As we have seen earlier, if the plates are not sufficiently separated, we must make a cor- 
rection since the trajectories of some electrons will not be fully used. This correction becomes 
more important when the radiation becomes more penetrating, for it then liberates more elec- 
trons of high energy, having long paths. 



202 



X national lab. 



1,000 



0,995 



B.I.RM. 
O 



® 



® 

t 



A 



AA 

t t t t 



10 kV 



) ▲ N.B.S. 
I A R.I.V. 



30 kV 50 kV 50 kV 

(b) (a) 

(• B.I.RM. 
B^O N.R.C. 
f® O.M.H. 



Figure 4. Some results of international comparisons in the field of low-energy x rays. The 
figure gives the exposure rates X measured at tiie BIPM by the standards of different na- 
tional laboratories, the BIPM standard being taken as reference. A: standards of small 
dimensions; B: standards of large dimensions. The figure shows a difference between the 
groups A and B. This difference is accentuated when the radiation becomes more penetrat- 
ing (the .50 kV radiation (a) is made more penetrating than the .50 kV radiation (b) of the 
same energy by interposing in the path of tiie beam, a supplementary disk of aluminum, 3 
mm thick, which stops the low-energy photons). 



Measurement of Gamma Radiation 

The y radiation from ""Co plays a particularly important role in 
dosimetry, both because it is used very much in medicine and because it 
forms a sort of link between the low and medium energies (< 1 MeV) and 
the high energies (1 to 50 MeV). Measurements at high energy are 
frequently based on calibrations made with y radiation from *"'Co. For this 
reason, the BIPM has chosen to give priority to measurements of this radia- 
tion. 



673-106 O - 75 - 15 



203 




Figure 5. Schematic section of the cavity chamber with graphite walls, at the BIPM. A: beam 
of y rays irradiating the entire chamber — this radiation liberates, in the graphite, electrons 
which ionize the air in the cavity; B: graphite collecting electrode (potential ~ 0); C: 
graphite walls at a potential of 80 V; the electric field ( — 40 000 V • m"') thus created 
between B and C allows collection of the ions produced in the cavity. The ions of one sign (+ 
in the case of the figure) terminate on electrode B: the charge they carry is measured by the 
device D. The chamber is cyhndrical: its circular faces are perpendicular to the axis A of 
the beam; the cavity volume is about 6.8 cm^. 



204 



Problems Posed by the Determination of 
Exposure for the y Radiation of^^Co 

A source of ''"Co emits photons of 1.17 and 1.33 MeV. The paths of 
electrons liberated by these photons can attain several metres in at- 
mospheric air. In this case, exposure measurement with an air-wall 
chamber at atmospheric pressure poses many problems. One can try to 
avoid them by increasing the pressure to reduce the chamber dimensions, 
but then other difficulties appear (loss by recombination of ions can reach 
10 percent if the pressure is of the order of 10 atmospheres). A different 
method would consist of utilizing a magnetic field created by a coil having 
the same axis as the photon beam: with a flux density of 0.25 T, the elec- 
trons can be kept in a cylinder of approximately 10-cm diameter [5]. Un- 
fortunately, this scheme permits the reduction of only the transverse 
dimensions (perpendicular to the beam axis) of the air-wall chamber. No 
solution using an air-wall chamber proves to be satisfactory. That is why 
the BIPM has chosen for its exposure standard a cavity chamber with gra- 
phite walls (fig. 5) in which several millimetres of graphite replaces several 
metres of air and is sufficient to assure "electron equilibrium." 

This substitution of graphite for air brings a modification of the elec- 
tron production which must first be considered. Moreover, one no longer 
operates in a simple medium: it is by virtue of the energy dissipated in one 
medium (air) by the electrons liberated in another medium (graphite) that 
there are ions to be measured. This results in a correction (called stopping 
power^ because the dissipation of energy of electrons in air is different 
from what it would be in graphite. The lack of accuracy (about 0.5%) of this 
correction constitutes the principal defect of cavity chambers. 

The Installation at the BIPM, and the Exposure Measurements 

Although several millimetres of lead suffices for protection against x 
rays of intermediate energy, a thickness of some 20 centimetres is needed 
when it is a question of the radiation emitted by a ''"Co source having an ac- 
tivity of several hundred curies such as those used for exposure measu- 
rements.** The BIPM therefore started by studying and having constructed 



^ For electrons of a given energy, the quotient dEjdl is caDed the stopping power S of a sub- 
stance, where dE is the energy lost by an electron of energy E in traversing an element of path 
of length dl in the substance considered. The electric charge due to ions produced in the air 
must be divided by / which is the mean value of (S/p) air/(S/p)Braphite, where p represents the 
mass density of the corresponding substance. 

» At 1 m from a source of 500 Ci, the exposure rate is about 10 R/min (which corresponds ap- 
proximately to an ionization current of 250 pA for a cavity chamber). After penetrating 
25 cm of lead, this exposure rate is reduced to less than 2 mR/h, which is less than the official 
permissable dose. 



205 



(1965) a lead "castle" capable of holding up to six radioactive sources. 
Figure 6 shows schematically the essentials of this device which was 
designed to reduce to a minimum the radiation scattered into the beam 
defined by the collimator. This castle received two sources of 1 Ci in 1966 
and one of 480 Ci (specific activity 400 Ci/g) in 1968.'' This last source is 
currently used for exposure measurements. 

The determination of exposure by use of a cavity chamber raises a cer- 
tain number of problems. Some have been mentioned above, but those are 
not the only ones: in particular, if one proposes to characterize the y-ray 
beam by means of the exposure which would exist in air in the absence of 
the chamber, it is necessary to know quantitatively the perturbation that 
the presence of the measuring instrument has on the quantity which one 
wishes to measure. This effect is usually studied by increasing the wall 
thickness of the chamber (above the 3 mm which is necessary to assure 
electron equilibrium) and extrapolating to zero thickness the variation ob- 
served in the ionization current as a function of wall thickness. By this 
procedure one measures in fact the superposed effects of several 
phenomena produced in the walls (photon attenuation and production of 
scattered photons of which some are in turn absorbed and contribute to the 
measured ionization) and the extrapolation is applied to the variation of a 




Figure 6. Schematic section of the lead castle for intense radioactive sources. Any of the 
sources contained in the barrel B can be chosen, then raised with the aid of an electric jack 
V to the source chamber C. The port H (lead glass) allows observation that the chosen 
source is correctly centered on the axis of the collimator D which limits the useful beam F. 
(To simplify the figure, many details, for example the device for rotating the barrel B, have 
been omitted.) 



^ These sources were given to the BIPM, those of 1 Ci by the National Research Council 
(Canada), that of 480 Ci by the National Bureau of Standards (U.S.A.). 



206 



sum whose different terms do not vary in the same manner with thickness. 
This is why we have tried to study these phenomena separately at the 
BIPM. For example, if we place a graphite disk either on the source side of 
the collimator aperture, or next to the chamber, the attenuation of photons 
stays the same but the ionization current is a httle larger in the second 
case, the difference corresponding to the contribution from scattered 
photons, In a general way, the BIPM has attacked the problem of the 
cavity chamber from a new angle by trying to approach as closely as possi- 
ble the conditions of the theoretical analysis [1]. For this reason, we have 
chosen a flat cylindrical cavity (fig. 5). Among the problems to be resolved, 
one of the most difficult is the following: how to take account of the non- 
uniformity of the radiation field in which are placed the chamber walls 
which produce the electrons, and in particular the nonuniformity of this 
field parallel to the beam axis, which becomes important if the cavity size 
is increased or if the chamber is closer to the source. This last problem has 
been studied theoretically [6] and experimentally by varying the source- 
chamber distance. Unfortunately, the role of the side walls of the chamber 
can not be analyzed validly in a simple way'^ and this probably increases 
the uncertainty of the determination of exposure by 0.3 percent. As for the 
reproducibility of measurement, it is excellent since the long-term standard 
deviation (for the most intense source), calculated for results extending 
over a year and a half, is equal to 10"^, allowing for weakening of the source 
whose half -life is 1926 days. 

International Comparisons of Exposure Standards for the ^^^Co y Radiation 

International comparisons have taken place at the BIPM between the 
standard chamber of the BIPM and some national standards of exposure 
(United States of America, Federal Republic of Germany, Netherlands, 
Hungary). These standards are also graphite cavity chambers but these 
chambers, with one exception, have forms and dimensions differing from 
that of the BIPM. Their total wall corrections are determined by the 
method indicated earUer. Figure 7 shows a satisfactory agreement, allow- 
ing for the uncertainties associated with different chambers. 

There do not appear to be any systematic differences due to the 
chamber geometries or to the methods of correcting for wall effects. Unfor- 
tunately, this type of comparison does not permit uncovering systematic er- 
rors involving the ratio / of the stopping powers of air and graphite. These 



For a disk of 3.3-mm thickness, the attenuation produces a loss of 3.6 percent and the scat- 
tered photons a gain of 2.0 percent. 

" The contribution of the side walls represents 14 percent of the total ionization measured. It 
was determined experimentally with a chamber similar to the standard chamber, but having 
side walls as thin as possible (0.5 mm). We added rings successively until electron equilibrium 
was reached and extrapolated the observed variation to zero thickness. 



207 



errors are practically the same for all graphite chambers, and therefore are 
eliminated when one determines the ratio of exposure measured by two of 
them. 



1,01 



^ X national lab./^ B.I.PM. 



1,00 



0,99 



0 



NBS 



PTB 



RIV 



OMH 



Figure 7. International comparison of exposure standards for the radiation from ""Co. The 
figure gives the exposure rates X measured at the BIPM by the standards of different na- 
tional laboratories, the BIPM standard being taken as reference. The error bars represent 
the estimates of systematic uncertainty (the random uncertainties are negligible). 

Comparison of Activity and Exposure Measurements 

The systematic errors which have just been noted can, on the contra- 
ry, be brought out when one compares, for a given cobalt source, measure- 
ments of two quantities of different kinds such as activity and exposure. 
Two photons (1.17 and 1.33 MeV) are emitted at each disintegration of an 
atom of ^"Co. The activity is the number of disintegrations per unit time; it 
thus permits knowledge of the incident energy of the photons crossing unit 
area per unit time at a given distance from the source. A known fraction'^ 
of this energy is transferred to the electrons liberated into the medium. 



This fraction is the coefficient of energy transfer, which is easily calculated from the proba- 
bilities of photoelectric and Compton interactions. 



208 



which we assume to be air. Knowing that a mean energy W is needed to 
produce a pair of ions in air, the corresponding ionization, and thus the ex- 
posure, is easily deduced. 

For this activity-exposure comparison, we use one of the two 1-curie 
sources (say 3.7 X 10'" s"'). Ahhough it corresponds to a small exposure 
rate, this activity is much too high to be measured directly. Measurement 
of the activity Ag of this source S was carried out by an original method 
utilizing a second source G of the same geometry, but having a much lower 
activity, Ag~2 mCi [7], as an intermediary. This method involves two 
steps: a) a relative measurement, the ratio /? ^y^sMc of the activities of the 
two sources; and b) an absolute measurement of the activity Aq. Measure- 
ment a) is made with a scintillation counter system. The sources G and S 
are placed at distances Dq~1 m and Dg = 23 m from the diaphragm limit- 
ing the useful beam so that the number of photons incident per unit time at 
the diaphragm is practically the same for the two sources; this eliminates 
many of the systematic errors.** The ratio R is given, to within a few cor- 
rections, by the ratio of the squares of the distances, Dg^lDc^, multiplied by 
the ratio of the pulse count rates, NglN,^. Measurement b) made by the 47r/3- 
y coincidence counting method, consists in determining the activities Am 
of a series of m very weak sources (about 0.2 ^lCi) obtained in the following 
way: the source G is dissolved in nitric acid and the solution is diluted in a 
known ratio, the sources m comprise small quantities of this diluted solu- 
tion, each containing a fraction 1/F(~ 10"*) of the source G. Aq is then the 
mean value of the products FA,,,, and Ag is the product RAq; this value Ag 
which one finally reaches is known with a good accuracy (better than 0.2%) 
despite all the intermediate steps brought into play.''' 

In comparing the measured exposure rate at a given distance from the 
source S to the calculated exposure rate based on the value Ag, a difference 
of 0.8 percent is found. This difference can arise either from the inaccuracy 
of the exposure measurement (due mainly to the ratio / of the stopping 
powers of air and graphite), or from the value of W{mea.n energy needed to 
produce a pair of ions) which had been used in the calculation of exposure 
rate from activity. It is therefore necessary to carry on the efforts to im- 
prove the accuracy of such constants as /and W. 

The detector is a crystal of sodium iodide in which part of the energy dissipated by the elec- 
trons liberated by the y-ray photons appears in the form of luminous energy: one observes 
flashes in the crystal, called scintillations, which are transformed into pulses of electric volt- 
age by means of a photomultiplier. An electronic device allows counting these pulses, whose 
total number is proportional to that of the y-ray photons striking the crystal. 

Note that without other precautions, the number of photons would be reduced by about 14 
percent in the case of the source S, by the additional 22 metres of air. To avoid this important 
correction, the beam passes down an evacuated pipe. 

■^The validity of this result is confirmed by the excellent agreement (0.02%) between the two 
values of the activity of a single source, one obtained by this method, the other by determining 
the power emitted by the source (calorimetric measurement at the National Bureau of Stan- 
dards) [8]. 



209 




Figure 8. Measurement of exposure and absorbed dose in graphite, for y radiation from ^°Co. 
A: standard cavity chamber for exposure measurements; B: graphite phantom whose front 
cover is shown in the foreground with the cavity chamber D used for measurement of ab- 
sorbed dose. 

Absorbed Dose 

In 1973, the BIPM commenced measurements of another quantity 
which is fundamental in dosimetry: absorbed dose, the energy dissipated 
per unit mass in a volume element of the material under consideration. The 
CCEMRI has chosen graphite as the reference material, the standard of 
absorbed dose being implicitly represented by a graphite cylinder of given 
dimensions (the name "phantom" assigned to this cylinder originates from 
medical reasons, for it simulates a human body with respect to the energy 
given it by radiation). 

The BIPM uses the ionization method (fig. 8), as for the measurement 
of exposure. If the energy W is known, the ionization produced permits cal- 
culation of the dose absorbed in the air of the cavity and from this is 
derived the dose absorbed in the graphite with the help of the ratio of 
stopping powers of graphite and air. The determination of this ratio is more 
complex in this case since the electrons are no longer liberated by only 1.17 
and 1.33 MeV photons: in fact, the deeper the beam penetrates into the 
phantom, the more it is enriched in scattered photons in proportion to its 
impoverishment in photons of 1.17 and 1.33 MeV. The photon spectrum 
has been calculated for the BIPM phantom by the Monte Carlo method, 

210 



simulating 25 000 photon "histories" with the aid of the IBM 1130 calcula- 
tor at the BIPM. Another problem to be resolved is that of the thickness of 
the chamber, whose cavity can not be likened to an elementary volume. It 
will be very fruitful to compare in the near future, the ionometric absorbed- 
dose standard of the BIPM with the standards of national laboratories, in 
particular with those which use the calorimetric method for measuring the 
energy imparted by the radiation. 



Bibliography 

[1] Allisy, A., Contribution a la mesure de Texposition produite par les photons einis parle 

""Co. Metrologia 3,41-51 (1967), and Recueil de Travaux du B.I.P.M. 1, (1966-1967). 
[2] Niatel, M.-T., An experimental study of ion recombination in parallel-plate free-air 

ionization chambers, Phys. Med. Biol. 12, pp. 555-563 (1967), and Recueil de Travaux 

du B.I.P.M. 1,(1966-1967). 
[3] Niatel, M,-T., Etude experimentale de Tinfluence de la vapeur d'eau sur I'ionisation 

produite dans I'air, C.R. Acad. Sci. Paris 268-B, pp. 1650-1653 (1969), and Recueil de 

Travaux du B.I.P.M. 2, article 22 (1968-1970). 
[4] Boutillon, M., Henry, W. H., and Lamperti, P. J., Comparison of exposure standards in 

the 10-50 kV x-ray region, Metrologia 5, pp. 1-11 (1969), and Recueil de Travaux du 

B.I.P.M. 2, article 21 (1968-1970). 
[5] Allisy, A. and Boutillon, M., Sur I'utilisation d'un champ d'induction magnetique dans 

les mesures d'exposition de rayons X et y, C.R. Acad. Sci. Paris 260, pp. 6576-6579 

(1965). 

[6] Boutillon, M., and Niatel, M.-T., A study of a graphite cavity chamber for absolute expo- 
sure measurements of ^"Co gamma rays, Metrologia 9, pp. 139-146 (1973), and Recueil 
de Travaux du B.I.P.M. 4, article 16 (1973-1974). 

[7] Roux, A.-M., A method of measuring the activity of a 1 Ci ''"Co source, Metrologia 10, 
99-102 (1974), and Recueil de Travaux du B.I.P.M. 4, article 17 (1973-1974). 

[8] Roux, A.-M., Comparison of activity and power measurements of a 1 Ci ''"Co source, 
Metrologia 10, 103-104 (1974), and Recueil de Travaux du B.I.P.M. 4, article 18 (1973- 
1974). 



211 



CHAPTER XI 



NEUTRON MEASUREMENTS 



Generalities 

Neutrons and protons, which are the constituents of atomic nuclei and 
thus of matter, resemble each other strongly in some respects. Neutrons, 
however, have no electric charge and thus they can pass without significant 
perturbation through the cloud of electrons which surrounds the nuclei of 
atoms. They can therefore easily penetrate matter without ionizing the 
atoms, and reach to the nuclei, causing nuclear reactions. These properties 
play an essential role in the production, detection, and utilization of 
neutrons. In particular, certain nuclear reactions which they produce 
release a very large amount of energy. It is especially the utilization of this 
energy on a large scale which brought about the urgent need for exact 
neutron measurements. 



Neutron Sources 

By bombarding light elements such as beryllium, boron, and lithium 
with helium nuclei {a particles), one can produce neutrons (n) by reactions 
denoted (a,n), for example: 

IBe + |He^»iC+ion, 

or according to the usual notation,^ "Be(a,n)i2C. Let us note in passing that 
it was this reaction which led J. Chadwick, in 1932, to the historic discovery 
of the neutron. Thus a mixture of beryllium and an a-particle emitter, such 
as radium or americium, provides a convenient (a,n) neutron source. 

Most nuclei are capable of emitting a neutron when struck by a suffi- 
ciently energetic y photon. For this (7,n) reaction to take place, the energy 
of the photon must be equal to or greater than the binding energy of the 



' This notation indicates, in order, the target nucleus (^Be), the incident particle (a), the 
ejected particle (n), and the final nucleus ('-C). The subscript, often omitted, indicates the 
number of protons (atomic number); the superscript is the sum of the numbers of protons and 
neutrons (mass number). 



213 



neutron; this energy is generally between 6 and 8 MeV, except for berylli- 
um (1.6 MeV) and deuterium (2.2 MeV): 

9Be + y ^ «Be + Jn ^ 2 |He + Vi 

?H + 7^ IH + Jn. 

Thus a capsule of radium surrounded by beryllium constitutes a currently 
used (7,n) source, the radium emitting a large number of y-rays of energy 
above 1.6 MeV. However the most used and most intense neutron sources 
at present are nuclear reactors. 

Neutrons produced by (a,n) and (y,n) sources or by nuclear reactors 
generally have a broad energy spectrum. In order to produce a beam of fast 
monoenergetic neutrons, charged particle accelerators are needed. Some 
of the reactions used with charged particle accelerators are: 

2H(d,n)3He, 3H(p,n)3He, 3H(d,n)4He, 

^Li(p,n)^e, i2C(d,n)i3N, »B(a,n)i4N, etc.^ 

Detection of Neutrons 

Since the neutron does not ionize the atoms it encounters, the usual 
methods of detection are not applicable and one must have recourse to 
other effects. The interaction of free neutrons with the matter they traverse 
is shown by their scattering and absorption. The scattering (elastic and in- 
elastic collisions) slows the neutrons which transfer energy to the nuclei 
they encounter; the nuclei can acquire, by recoil, enough energy to 
produce ions. The absorption of neutrons causes nuclear transformations. 
Essentially three types of detection are seen: a) by collision, particularly by 
elastic collision of fast neutrons with protons; the kinetic energy of the 
neutrons is partially converted to recoil energy of protons which can then 
be measured through ionization produced or by light emitted; b) by count- 
ing light particles (p, d, a, ...) produced in the course of a nuclear reaction; 
c) by analysis of resulting products (chemical analysis, analysis by the 
radioactivity produced, etc.). 

Neutron Measurements 

When a beam of neutrons is incident on a target (a body containing a 
large number of atoms of a certain kind), only a small fraction of the in- 
cident neutrons passes sufficiently close to target atoms for the reaction 
under study to take place. The beam is characterized by its flux density <E>, 



-p = 'H = proton (hydrogen nucleus): d = -H = deuteron (deuterium nucleus): ■'H = triton 
(tritium nucleus); a = ^He (nucleus of helium-4); ^He = (nucleus of helium-3). 



214 



the number of neutrons crossing a unit area per unit time. If the target con- 
tains a total number of nuclei and if each of these nuclei presents an area 
cr to the beam, the mean number of times per second that a nucleus in- 
teracts with a neutron is equal to the product N'^cr and is called the reac- 
tion rate. The quantity cr, called the cross section for this reaction, must not 
be confused with the (very small) geometric cross section of the nuclei or of 
the neutron; it is a fictitious area which in fact measures the probability of 
occurrence of the reaction under consideration. 

The measurement of cross sections holds a very important position in 
the field of neutron measurements and requires the determination of 
neutron flux density (there is however one exception: the cross section 
multiplied by the number of nuclei per unit volume in an absorber gives the 
attenuation coefficient; this latter can be determined by measurements of 
transmission through a sheet of material, which requires only the measure- 
ment of a ratio of flux densities). 

Furthermore, precise measurements of flux density are also necessary 
for standardizing detectors used in various fields (nuclear physics, neutron 
dosimetry, protection against ionizing radiation, industry, etc.). This quan- 
tity has been judged sufficiently important for the BIPM to undertake a 
program in this area. The BIPM has for this purpose two types of neutron 
sources which will be described in the following sections, along with the 
methods used to measure neutron flux density. 



Measurement of the Emission Rate of a Neutron Source by the 
Manganous Sulfate Bath Method 

Here we are concerned with neutron sources of the types (a,n) or (7,n) 
which use long half-life radioactive emitters such as radium (1600 years) or 
americium (433 years). The emission rate of such a source is defined by the 
number of neutrons emitted per second (into all directions). Figure 1 gives 
the dimensions and compositions of four neutron sources of this kind pos- 
sessed by the BIPM. 

Measurements of emission rate of these neutron sources are carried 
out by a classical method of total absorption of the neutrons in a concen- 
trated aqueous solution of manganous sulfate. The fast neutrons emitted by 
the source are first slowed down, primarily by scattering by hydrogen; they 
then have a high probabihty of being captured when they are in thermal 
equihbrium with the medium (thermal neutrons). The dimensions of the 
spheres which contain the manganous sulfate solution are chosen accord- 
ing to the energy spectrum of the neutrons emitted by the source to be 
measured, to be large enough to reduce the loss of neutrons from the 
sphere to an acceptable value; for (a,n) sources whose spectrum extends 
up to a maximum energy of 12 MeV, the sphere has a diameter of 1 m and 



215 



Reaction 
type 



Radio; 
nuclide 

a or Y 

and 
Gcti vity 
(in Ci) 



Capsule 
material 



Neutron 
emission 
rate 

(in 10^ s-\ 
Oct. 1969) 



Source 
construction 
scale 

2 cm 



Be ( a , n : 



226 



Ra 

0,2 



mone I 
l68% NI, 
29% Cu, 
2% Fe, 
1% Mn) 



monel 



3,27 



Be + Ra 



Be I y , n ) 



Re ( (V, ni 



Be I a , n, 



226 



Ra 
0,5 



0, 448 



mone 1 



241 



Am 



stainless 
steel 



241 



Am 

0,1 



stainless 
steel 




= 0,22 



Figure 1. The BIPM neutron sources. 



216 



the neutron loss is of the order of 1 percent; for the Ra-Be (7,n) source, 
whose spectrum extends up to a maximum energy of 700 keV, a 50 cm 
diameter sphere is used and the loss of neutrons is negligible. If a neutron 
is captured by a nucleus of ^^Mn, the nucleus is transformed into ^^Fe, ac- 
cording to the scheme: 

55Mn + n ^ '^^Mn 5«Fe* ^ ^«Fe 

where the asterisk indicates an excited state. If a neutron is captured by a 
hydrogen nucleus, a deuteron (stable) is formed. Capture by other atomic 
nuclei present in the solution is much less frequent. 

The disintegration scheme of ^^Mn is represented in figure 2. The 
emission rate for neutrons from the source Q is equal to the sum of the cap- 
ture rates for neutrons in the solution and in the source (self-absorption), 
and of the rate of escape of neutrons from the solution. One thus has 

where is the number of neutrons captured per second by the man- 
ganese nuclei in the solution, /is the ratio of the number of neutrons cap- 
tured by manganese nuclei to the number of neutrons captured by the 
totality of elements contained in the solution {f ~ 0.5), A: is a correction fac- 
tor to allow for systematic errors due to the absorption of neutrons (espe- 
cially slow ones) in the source due to the presence of the bath, to the ab- 




Figure 2. Disintegration scheme for ^•^Mn. The nucleus transforms itself by emission of a ^- 
particle (oblique arrows) into ^Te in an excited state: the latter then loses its excess energy 
by emitting a photon of y radiation (vertical arrows). The horizontal lines correspond to the 
energy levels of the nuclei. 



217 



sorption of fast neutrons by oxygen and sulfur in the solution, to impurities 
in the solution, and to the escape of neutrons from the manganese bath {k = 
1.04). 

For irradiation to saturation, that is to say for an irradiation time t long 
in comparison to the half-life of ■'''*Mn {T112 =2.6 hours), as many neutrons 
are being captured by the ■"'■'"'Mn as there are •^'^Mn nuclei disintegrating, and 
the disintegration rate Q' at the moment the source is withdrawn from 
the solution (time f' = 0), is equal to ^Mn- In practice, the source is 
withdrawn at the end of a time t ~\6\\, and at time ^' = 0 we have: 

<?'Mn (0 = <?Mn ( 1 - 6 "^0 = 0.9865 (?Mn 

where A = ln 2/ri/2 = 0.2688 h-i. 

In order to measure the relative activity of the irradiated solution, y- 
rays emitted by the ''"Fe* are counted by means of a scintillation detector 
(sodium iodide crystal) immersed in the bath in place of the source. This 
relative measurement of activity is completed by an absolute calibration: 
after the bath has lost its activity, a quantity of active ^"Mn solution, whose 
specific activity has been previously determined by the method of 477/3-7 
coincidence counting is added to the bath. We then have 

source)/ (Psolution) ■< 

where Psource designates the counting rate obtained in the irradiated man- 
ganese bath, and Psoiution is the rate obtained after adding a solution of ac- 
tivity A to the bath. 

For measurement of Ra-Be (y,n) sources, we have also set up a variant 
of the manganese bath method. It involves measuring the activity of the 
manganous sulfate solution outside the sphere in which the solution is con- 
tinuously irradiated by the source to be measured. A pump circulates the 
solution in a closed circuit (flow of 6 htres per minute) between the sphere 
and an enclosure 10 metres away (fig. 3). This enclosure is protected from 
y-rays from the source by a 40-cm thick concrete wall and by a lead shield 
with wall thickness of 10 cm; in this shielded location the measurements of 
the activity of the irradiated solution are made. This new technique, called 
the circulation method, lends itself particularly well to the measurement of 
relatively low intensity neutron sources. 

Comparative Measurements of Neutron Sources 

It is planned that the neutron sources belonging to the BIPM remain 
there permanently. National laboratories which desire to have their own 
sources compared can send them to the BIPM; the BIPM can however or- 
ganize international comparisons using sources furnished by other labora- 
tories, as in the following example. 



218 




Figure 3. Measurement of the emission rate of a neutron source by the metliod of circulation 
of a manganous sulfate solution. A: sphere (d = 50 cm) containing the solution; B: (y,n) 
source; C: stirrers; D: circulation pump; E: counting beaker placed 10 m from the sphere; 
F: sodium iodide crystal; G: photomultipUer; H: lead shield (wall thickness : 10 cm); I: 
concrete wall (thickness : 40 cm). 



Standard Ra-Re (a,n) Source No. 200-1 of the 
National Research Council of Canada 

Measurements of the emission rate of this source, made by the man- 
ganese bath method from January 1962 to March 1965 by 10 participating 
laboratories [1], gave a 3 percent maximum spread among the results. The 
total uncertainty estimated by the participants varied between ±0.7 and± 
1.7 percent (fig. 4). The manganese bath method, adopted by most of these 
laboratories, is considered to be the method capable of the best precision 
in measuring the emission rate of a neutron source. 

Standard Ra-Be (a,n) andRa-Be (y,n) Sources of the BIPM 

The standard Ra-Be (a;,n) source (fig. 1) has been measured periodi- 
cally at the BIPM since December 1963, by the manganese bath method; 
the consistency of the measurements is' very satisfactory. Currently, the 
reproducibility of measurement is 0.1 percent, while the accuracy of the 
emission rate of the source is 1 percent. The principal sources of error are 



573-106 O - 75 - 16 



219 



Participating 
laboratory 



3,1 



3,2 
— h- 



Neutron emission rote 
f- 



3,3 



3,4-10^S-^ 



ETL 

LKO 

CENS 

IMM 

SRE 

BCMN 

BIPM 



-O- 



AEET 
NRC 



NBS 



NPL 



mean value 



-O 



I — o 



1% 

I 1 



Figure 4. Results of measurements of emission rate of the Ra-Be (a,n) neutron source No. 
200-1 of the NRC, normaUzed to reference cross sections and to January 1962. The labora- 
tories are listed in the order of the dates of measurement (January 1962 to February 1965). 
The measurement by the NPL dates from June 1959. The bars indicate the total uncertain- 
ties estimated by the participants. 



the uncertainties in the capture cross sections for thermal and fast 
neutrons, and in the correction factors. 

As for the standard Ra-Be (7,n) source (fig. 1), the emission factor has 
been determined with an accuracy of 0.5 percent. In fact, the Ra-Be (y,n) 
sources have the advantage over the Ra-Be (a,n) sources of not needing 
correction for absorption by the (n,p) and (n,a) reactions with oxygen and 
sulfur, the upper neutron energy limit of 700 keV being below the threshold 
for these reactions. 



220 



Measurement of the Flux Density of a Source 
of Fast Monoenergetic Neutrons 

The BIPM has undertaken the study of a neutron source using the 
reaction 2H(d,n)^He. This source, which emits relatively monoenergetic 
fast neutrons of 2.5 MeV, can in fact be studied with rather modest experi- 
mental facilities; the source also emits, in association with the neutrons, 
charged ^He particles which can be detected in order to measure the 
neutron flux density in a given direction by the associated particle method. 

The principle of this measurement method is the following: the emis- 
sion of each neutron corresponds to the emission of a ^He particle in the op- 
posite direction in the center-of-mass system;^ in other words, in the system 
of the center-of-mass, the number of ^He particles emitted per unit solid 
angle in a given direction must be equal to the number of neutrons emitted 
per unit solid angle in the opposite direction. It is therefore possible to 
measure the neutron flux density in a given direction either by counting the 
^He particles (with an efficiency of 100%) by means of a surface-barrier 
semiconductor detector, or by the counting of neutrons by means of a scin- 
tillation counter (hydrogenous scintillator) whose efficiency has been mea- 
sured. These two relatively independent methods can be used simultane- 
ously to compare the results obtained. 

Let us designate by 4>He the number of neutrons measured by counting 
the ^He particles in the solid angle Cl^ covered by the neutron detector. If 
kiie and are the factors for converting solid angles from the laboratory 
system (SI) to the center-of-mass system (ft'), for ^He particles and 
neutrons respectively, and if A'^He is the total number of ^He particles 
counted with the use of the semiconductor detector which covers the solid 
angle Ctue^ we can write: 

^^n~ ^n^^'n^ ^^He~ ^He ^ Hei 
fine 

On the other hand, if represents the number of neutrons emitted in 
Sin and A^n the number of neutrons counted by the hydrogen scintillation 
counter of efficiency e, we can write 

^n = (NJe)f. 

The factor / takes account of effects such as: neutron scattering, 
anisotropy of the source, emission of neutrons by secondary sources, etc. 
We determine the efficiency e in the course of the same series of measure- 
ments, by counting, in addition to A^He and A^n, the coincidences of ^He par- 



' The center-of-mass system is the reference system in which the center of mass of all the parti- 
cles participating in the reaction is taken as the origin. This system is not at rest relative to the 
laboratory frame-of-reference, but it has the advantage of making the formulas particularly 
simple for calculating speeds and angles. 



221 




Figure 5. Diagram of experimental arrangement for measurement of the flux density of a 
-H(d.n)'He neutron source; comparison of the two methods (direct detection and associated 
particle). A; beam of accelerated deuterons (100 keV); B: aperture, d = 12 mm; C: 
vacuum chamber of magnetic analyzer; D: magnetic field; E: aperture. d=10 mm; F: 
quadrupole electrostatic lens; G: aperture, d = 5 mm; H: target (neutron source) of deu- 
terated titanium; J; semiconductor detector for ^He particles; K: hydrogenous scintillator, 
neutron detector; L: distance of 1.2 m. 

The ensemble B to G serves to eUminate molecular ions from the beam and to concen- 
trate the deuterons on the target by magnetic separation. When an angle of 90° is chosen for 
observation of ^He particles, the neutron detector must be located at 77° to count the 
neutrons associated with these particles. 



222 



tides and neutrons. Finally, it is a matter of comparing the two quantities 
4>He and $n which should be equal. 

Figure 5 shows the experimental arrangement which includes an elec- 
trostatic accelerator (150 kV, 2mA). Experiments have been carried out 
[2,3] with a beam of 100 keV deuterons and a target current of 2 /liA (emis- 
sion rate of the source ~ 10^ s"'), observing the ^He particles at 150°, 120°, 
and 90° (in the laboratory reference system). The flux densities of neutrons 
of 2.76 MeV, 2.67 MeV, and 2.53 MeV have been measured by each of the 
two detectors with an uncertainty of ±2 percent. In comparing the values 
of $He and we have been able to determine that when the target is per- 
pendicular to the direction of the incident deuteron beam (observation of 
'^He particles at 150° and 120°), there has been a satisfactory agreement 
between and on the contrary, a disagreement has appeared (<!>„ > 
4>He) when the target is inclined at 45° (differences of + 4.2 percent for the 
observation of ^He particles at 90° and of + 3.1 percent for observation at 
120°); none of the interpretations considered until now to explain this dis- 
crepancy has been satisfactory. 

To compare measurements of neutron flux density among various 
laboratories, the use of rather simple and rugged, but relatively insensitive, 
transfer instruments is anticipated. The participation of the BIPM in such 
comparisons being highly desirable, a considerable increase in the emis- 
sion rate of the '^H(d,n)''He neutron source has become indispensable. With 
an incident deuteron energy of 140 keV and a target current of 200 ^lA (tar- 
get cooled by a jet of nitrogen whose temperature is slightly below 0 °C), it 
has been possible to increase the maximum emission rate for neutrons 
from this source to 4 X 10^ s"' in the solid angle 477 steradian [2]. 

The results obtained with the lower emission rate, although not yet 
satisfactory, seem to indicate that the absolute measurement of a 
^H(d,n)^He neutron source by the associated particle method does not pose 
insoluble problems. The future should show if the precision and consisten- 
cy of these measurements can be increased enough that the results can be 
comparable to those of measurements of the same source by a neutron 
slowing-down method. 



223 



Bibliography 



[1] Naggiar, V., Rapport sur la comparaison internationale de la mesure du taux d'emission 
de la source de neutrons Ra-Be (a,n) du Conseil National de Recherches No. 200-1 par 
la methode de ralentissement des neutrons dans une solution de sulfate de manganese 
(fevrier 1967), Recueil de Travaux du B.I.P.M. 1 , 48 pages (1966-1967). 

[2] Huynh, V. D., Lafaye, L., and Breonce, P., dans Proces-Verbaux C.I.P.M. 40, pp. 75-82 
(1972). 

[3] Naggiar, V., Lafaye, L., and Breonce, P., Distribution angulaire d'une source de 
neutrons D(d,n)^He en cible epaisse pour deutons de 100 keV, Nucl. Instr. and Meth. 
41, pp. 77-83(1966). 



224 



Appendix 1 



Convention of the Metre' 
(May 20, 1875) 

His Excellency the President of the French Republic, His Majesty the 
Emperor of Germany, His Majesty the Emperor of Austria-Hungary, His 
Majesty the King of the Belgians, His Majesty the Emperor of Brazil, His 
Excellency the President of the Argentine Confederation, His Majesty the 
King of Denmark, His Majesty the King of Spain, His Excellency the Pre- 
sident of the United States of America, His Majesty the King of Italy, His 
Excellency the President of the Repubhc of Peru, His Majesty the King of 
Portugal and the Algarves, His Majesty the Emperor of all the Russias, His 
Majesty the King of Sweden and Norway, His Excellency the President of 
the Swiss Confederation, His Majesty the Emperor of the Ottomans, and 
His Excellency the President of the Repubhc of Venezuela, desiring inter- 
national uniformity and precision in standards of weight and measure, have 
resolved to conclude a convention to this effect, and have named as their 
plenipotentiaries the following: 

His Excellency the President of the United States of America: Mr. 
Ehhu Benjamin Washburne, Envoy Extraordinary and Minister 
Plenipotentiary of the United States at Paris; 

His Majesty the Emperor of Germany: His Highness Prince Hohen- 
lohe Schillingsfiirst, Grand Cross of the Order of the Red Eagle of Prussia, 
and of the Order of St. Hubert of Bavaria, &c., &c., &c., his Ambassador 
Extraordinary and Plenipotentiary at Paris; 

His Majesty the Emperor of Austria-Hungary: His Excellency Count 
Apponyi, his current Chamberlain and Privy Counselor, Knight of the Gol- 
den Fleece, Grand Cross of the Royal Order of St. Stephen of Hungary, and 
of the Imperial Order of Leopold, &c., &c., &c., his Ambassador Extraor- 
dinary and Plenipotentiary at Paris; 

His Majesty the King of the Belgians: Baron Beyens, Grand Officer of 
his Order of Leopold, Grand Officer of the Legion of Honor, &c., &c., &c., 
his Envoy Extraordinary and Minister Plenipotentiary at Paris; 

His Majesty the Emperor of Brazil: Mr. Marcos Antonio d'Araujo, 
Viscount d'ltajuba. Grandee of the Empire, member of His Majesty's 
Council, Commander of his Order of Christ, Grand Officer of the Legion of 



' Articles preceded by the sign ► have been modified, or supplemented, by the International 
Convention of 1921 (see p. 230). 



225 



Honor. &c., &c., &c., his Envoy Extraordinary and Minister Plenipotentia- 
ry at Paris; 

His Excellency the President of the Argentine Confederation: Mr. Bal- 
carce. Envoy Extraordinary and Minister Plenipotentiary of the Argentine 
Confederation at Paris; 

His Majesty the King of Denmark: Count de Moltke-Hvitfeldt, Grand 
Cross of the Order of Dannebrog, and decorated with the Cross of Honor of 
the same order. Grand Officer of the Legion of Honor, &c., &c., &c., his 
Envoy Extraordinary and Minister Plenipotentiary at Paris; 

His Majesty the King of Spain: His Excellency Don Mariano Roca de 
Togores, Marquis de MoHns, Viscount de Rocamora, Grandee of Spain of 
the First Class, Knight of the Renowned Order of the Golden Fleece, Grand 
Cross of the Legion of Honor, &c., &c., &c.. Director of the Royal Spanish 
Academy, his Ambassador Extraordinary and Plenipotentiary at Paris; and 

General Ibaiiez, Grand Cross of the Order of Isabella the Catholic, 
&c., &c.. Director General of the Geographical and Statistical Institute of 
Spain, Member of the Academy of Sciences; 

His Excellency the President of the French Republic: The Duke 
Decazes, deputy to the National Assembly, Commander of the Order of the 
Legion of Honor, &c., &c., &c.. Minister of Foreign Affairs; 

the Viscount de Meaux, deputy to the National Assembly, Minister of 
Agriculture and of Commerce; and 

Mr. Dumas, Perpetual Secretary to the Academy of Sciences, Grand 
Cross of the Order of the Legion of Honor; 

His Majesty the King of Italy: The Chevalier Constantin Nigra, Knight 
of the Grand Cross of his Orders of St. Maurice and St. Lazarus, and of the 
Crown of Italy, Grand Officer of the Legion of Honor, &c., &c., &c., his 
Envoy Extraordinary and Minister Plenipotentiary at Paris; 

His Excellency the President of the Republic of Peru: Mr. Pedro Gal- 
vez. Envoy Extraordinary and Minister Plenipotentiary of Peru at Paris; 
and Mr. Francisco de Rivero, formerly Envoy Extraordinary and Minister 
Plenipotentiary of Peru; 

His Majesty the King of Portugal and of the Algarves: Mr. Jose da 
Silva Mendes Leal, Peer of the Realm, Grand Cross of the Order of Saint 
James, Knight of the Order of the Tower and Sword of Portugal, &c., &c., 
&c., his Envoy Extraordinary and Minister Plenipotentiary at Paris; 

His Majesty the Emperor of all the Russias: Mr. Gregory Okouneff, 
Knight of the Russian Orders of St. Anne of the first class, of St. Stanislaus 
of the first class, of St. Vladimir of the third. Commander of the Legion of 
Honor, current Counselor of State, Counselor of the Embassy of Russia at 
Paris; 

His Majesty the King of Sweden and Norway: Baron Adelsward, 
Grand Cross of the Order of the Polar Star of Sweden, and of St. Olaf of 
Norway, Grand Officer of the Legion of Honor, &c., &c., &c., his Envoy 
Extraordinary and Minister Plenipotentiary at Paris; 



226 



His Excellency the President of the Swiss Confederation: Mr. Jean 
Conrad Kern, Envoy Extraordinary and Minister Plenipotentiary of the 
Swiss Confederation at Paris; 

His Majesty the Emperor of the Ottomans: Husny Bey, Lieutenant- 
Colonel of Staff, wearer of a fourth-class decoration of the Imperial Order 
of Osmania, of a fifth-class decoration of the Order of Medjidie, Officer of 
the Legion of Honor, &c., &c., &c.; 

His Excellency the President of the Republic of Venezuela: Doctor 
Eliseo Acosta, 

Who, after having exhibited their full powers, which were found to be 
in good and due form, have agreed upon the following articles: 

Article L 

The high contracting parties engage to establish stnd maintain, at their 
common expense, a scientific and permanent international bureau of 
weights and measures, the location of which shall be at Paris. 

Article 2. 

The French Government shall take all the necessary measures to 
facilitate the purchase, or, if expedient, the construction, of a building 
which shall be especially devoted to this purpose, subject to the conditions, 
stated in the regulations which are subjoined to this convention. 

Article 3. 

The operation of the international bureau shall be under the exclusive 
direction and supervision of an international committee for weights and 
measures, which latter shall be under the control of a general conference 
on weights and measures, to be composed of the delegates of all the con- 
tracting governments. 

Article 4. 

The general conference on weights and measures shall be presided 
over by the president for the time being of the Paris Academy of Sciences. 

Article 5. 

The organization of the bureau, as well as the formation and the 
powers of the international committee, and of the general conference on 
weights and measures, are established by the regulations subjoined to this 
convention. 



227 



Article 6. 



The international bureau of weights and measures shall be charged 
with the following duties: 

1st. All comparisons and verifications of the new prototypes of the 
metre and kilogram. 

2d. The custody of the international prototypes. 

3d. The periodic comparison of the national standards with the inter- 
national prototypes and with their test copies,^ as well as comparisons of 
the standard thermometers. 

4th. The comparison of the prototypes with the fundamental stan- 
dards of non-metric weights and measures used in different countries for 
scientific purposes. 

5th. The sealing and comparison of geodetic measuring-bars. 

6th. The comparison of standards and scales of precision, the verifica- 
tion of which may be requested by governments or by scientific societies, 
or even by constructors or men of science. 

► Article 7. 

The persons composing the bureau shall be a director, two assistants, 
and the necessary number of employees. 

When the comparisons of the new prototypes shall have been finished, 
and when these prototypes shall have been distributed among the different 
states, the number of persons composing the bureau shall be reduced so far 
as may be deemed expedient. 

The governments of the high contracting parties will be informed by 
the international committee of the appointment of the persons composing 
this bureau. 

► Article 8. 

The international prototypes of the metre and of the kilogram, together 
with the test copies- of the same, shall be deposited in the bureau, and ac- 
cess to them shall be allowed to the international committee only. 

Article 9. 

The entire expense of the construction and outfit of the international 
bureau of weights and measures, together with the annual cost of its main- 
tenance and the expenses of the committee, shall be defrayed by contribu- 
tions from the contracting states, the amount of which shall be computed 
in proportion to the actual population of each. 



'-' Editor's note: Modern terminology is "check standards." 



228 



Article 10. 



The amounts representing the contributions of each of the contracting 
states shall be paid at the beginning of each year, through the ministry of 
foreign affairs of France, into the Caisse de depots et consignations at Paris, 
whence they may be drawn as occasion may require, upon the order of the 
director of the bureau. 

► Article 11. 

Those governments which may take advantage of the privilege, open 
to every state, of acceding to this convention, shall be required to pay a 
contribution, the amount of which shall be fixed by the committee on the 
basis established in article 9, and which shall be devoted to the improve- 
ment of the scientific apparatus of the bureau. 

Article 12. 

The high contracting parties reserve to themselves the power of in- 
troducing into the present convention, by common consent, any modifica- 
tions the propriety of which may have been shown by experience. 

Article 13. 

At the expiration of 12 years this convention may be abrogated by any 
one of the high contracting parties, so far as it is concerned. 

Any government which may avail itself of the right of terminating this 
convention, so far as it is concerned, shall be required to give notice of its 
intentions one year in advance, and by so doing shall renounce all rights of 
joint ownership in the international prototypes and in the bureau. 

Article 14. 

This Convention shall be ratified according to the constitutional laws 
of each state, and the ratifications shall be exchanged in Paris within 6 
months, or sooner, if possible. It shall take effect on the first day of January 
1876. 

In testimony whereof the respective plenipotentiaries have attached 
their signatures and have hereunto affixed their seals of arms. 

Done at Paris, May 20, 1875. (The seals and signatures of the 
plenipotentiaries follow.) 



229 



This Convention was modified slightly by the international Convention 
signed at Sevres on October 6, 1921. 
Article 7 became: 

After the Committee shall have proceeded with the work of coordinat- 
ing the measures relative to electric units and when the general conference 
shall have so decided by a unanimous vote, the Bureau will have charge of 
the establishment and keeping of the standards of the electric units and 
their test copies and also of comparing with those standards, the national 
or other standards of precision. 

The Bureau is also charged with the duty of making the determina- 
tions relative to physical constants, a more accurate knowledge of which 
may be useful in increasing precision and further insuring uniformity in the 
provinces to which the above mentioned units belong (Article 6 and 1st 
paragraph of Article 7). 

It is finally charged with the duty of coordinating similar determina- 
tions effected in other institutions. 

In Article 8, the words "of the metre and of the kilogram" were 
deleted. 

Article 11 was supplemented as follows: 

Any state may adhere to this convention by giving notice thereof to the 
French Government which shall notify all the participant states and the 
Chairman of the International Committee for Weights and Measures. 

Any new accession to the Convention of May 20, 1875, will necessarily 
involve adherence to this Convention. 

Regulations are annexed to the Convention of 1875; they have the 
same force and value as the Convention itself. These regulations, which 
were modified in 1907, 1921, and 1960, estabhsh in particular: 

— Requirements on construction, equipment, and operation of the 
BIPM (buildings, instruments, budgetary rules). 

— The role of the CGPM (dissemination and improvement of the 
metric system, ratification of fundamental metrological determina- 
tions, election to the CIPM), the voting rules and the distribution of 
financial expenses among the States. 

— The composition, renewal procedures, and operation of the 
CIPM as well as its mission (direction of the work and operations of 
the BIPM, nomination of the director and some assistants, 
estabhshment of the budget, setting calibration fees, surveillance of 
the prototypes, annual report to the Governments). 

— The conditions for access to the place of deposit of the proto- 
types and of publication (in French) of reports and work of the BIPM 
and CIPM. 



230 



Appendix 2 



Member States of the Metre Convention 
1875 Signatories 



PortU" 



Ar};eiitiiia 

Auslria-HuiiKary p 
Bel);iuni 
Brazil 
Denmark 
France 



Spain 

Sweden and Norway 
Svvllzerland 
Turkey 

Germany V.SA. 

''^'y Venezuela 
Peru* 



Austria 

Bel);ium 

Brazil' 



Member States as of January 1, 1975 
(43 States) and Dates of Adherence 



Argentina 1875 

Australia 1947 

'1875 
1875 
1954 

Bulgaria jgjj 

Cameroon 1971 

Canada 1907 

Chile 19Q8 

Czechoslovakia 1922 

Denmark 1875 

Dominican Republic 1954 

Efjypt 1952 

Finland 1921 

France I875 

German Democratic Republic 1875 

Germany (Fed. Rep. of) 1875 

Hungary I875 

India 1957 

Indonesia 1960 

Ireland 1926 

'laly ^ 1875 

Japan 1885 

Korea (Rep. of) 1959 

Mexico 1890 



ilhilriM in 1456 

' Brazil ralifii-.l il> IH75 acllu-r r in 1 ami «illi.ir,.« in 1<>32. 



231 



NothorlaiuI> (The) 


1929 


Norway 


187.5 


Pakistan 


197.3 


Poland 


1925 


Porlu"'aI 


1875 


Hoiiian ia 


188.3 


Spain 


1875 


S)>nth Africa 


1964 


Swrdrii 


1875 


t.JT\ H/A 1 1(111(1 


1875 


1 Hull clll < 1 


1912 


Turltcy ^ 


193.3 


U.S.S.R. 


1875 


United Kiiif;ilorii 


1884 


U.S.A. 


1875 


Uruf;uay 


1908 


Venezuela' 


1960 




1879 



'Turkfv.dll 1875 ^-ifiiialon. 4\ilh<irevfc in 1889. 

* Si^Iiiaiitrv ill 1875. adherence nul iiiaiiilaiiieii in I9U6. 



232 



Appendix 3 



Members and Officers of the CIPM, 
and Directors of the BiPM 
from 1875 to 1975 
(in chronological order) 

Members of the CIPM 



One hundred and ten noted scientists have served on the CIPM since its incepti 



Bo^scha. J.. Delll. The Netherlands' 


1875 


Broeh, 0. J.. Christiana, Norway 


1875-1889 


Chisholm, H. W., London. Great Britain' 


1875 


Foerster, W., Berlin, Germany 


1875-1921 


Govi, G., Turin. Italy 


1875-1889 


Herr, J., Vienna. Austria 


1875-1884 


Hilgard, J. E., Washington, D.C.. U.S.A. 


1875-1887 


Hirsch, A., Neuchatel, Switzerland 


1875-1901 


Husny-Bey, Constantinople, Turkey 


1875-1883 


Ibanez, C, Madrid. Spain 


1875-1891 


Morin, A., Paris, France 


1875-1880 


Stas, J.-S, Brussels. Belgium 


1875-1891 


Wild, H., St. Petersburg, Russia 


1875-1895 


Wrede, Baron de, Stockliolni Sweden 


1873-1885 


Gould, B.-A., Cordova. Argentina 


1879-1884 


Krusper, E. de. Pest, Hungary 


1879-1894 


Dumas, J.-B., Paris, France 


1880-1884 


Aguiar, A. de, Lisbon, Portugal 


1884-1887 


Bertrand, J., Paris, France 


1884-1900 


Christie. W.-H.. Greenwich. Great Britain 


1885-1891 


Oppolzer. Th. von. Vienna. Austria 


1885-1886 


Thalen, R., Uppsala, Sweden 


1885-1900 


Gould. B.-A., Cambridge, U.S.A. 


1887-1896 


Lang. V. von, Vienna, Austria 


1887-1921 


Macedo, H. de, Lisbon, Portugal 


1887-1901 


Amdsten, A.. Christiana, Norway 


1889-1913 


Brioschi, J., Rome, Italy 


1889-1895 


Chaney, H.-J., London, Great Britain 


1891-1906 


Arrillaga. F. de P., Madrid, Spain 


1894-1920 


Bodola. L. de, Budapest, Hungary 


1894-1929 


Hepiles. Sl.-C. Bucharest. Romania 


1894-1922 


Ferraris, G., Turin, Italy 


1895-1897 


Mendeleyev, D., St. Petersburg, Russia 


1895-1901 


' Thf Nerh«>riaii(l> and Great Britain not having >i^'iieri the Metre ('(nnenlinii in 1875. J. B<>s>rha ar 


(1 11. ^. <:hi>h<ilni revif£ne<l fn.ni tlie 


CIPM, 





233 



Blaserna. P., Rome, Italy 

Michelson, A. A., Chieajjo, U.S.A. 

Comu. A., Paris, France 

Hasselberf;, K.-B., Stockholm, Sweden 

E};oroff, N., St. PetersbuTf;, Russia 

Gaulier, R., Geneva, Switzerland 

Mascarl, E., Paris, France 

Slralton, S. W., Boston, U.S.A. 

Gill, Sir David, London, Great Britain 

Tanakadate, A., Tokyo, Japan 

Darboux, J.-G., Paris, France 

Appell, P.. Paris, France 

MacMahon, P. A., London, Great Britain 

Pasquier, E., Louvain, Bel(;ium 

Volterra, V., Rome, Italy 

Rosters, W., Berlin, Germany 

Torres y Quevedo, L., Madrid, Spain 

Isaachsen, D., Oslo, Norway 

Fredholm, E.-L, Stockholm, Sweden 

Karfjatchin. C. Belgrade, Yiifjoslavia 

Konovalov, D.. Leninjjrad, U.S.S.R. 

Cabrera, B., Madrid, Spain 

Johansen, E. S., Copenhagen, Denmark 

MacLenan, J. C, Toronto, Canada 

Posejpal, v., Pra(;ue. Czechoslovakia 

Chatelain, M., Lelingrad. U.S.S.R. 

Statescu, C, Bucharest. Romania 

Zeeman, P., Amsterdam, The Netherlands 

Sears, J. E., Teddington-London, United Kingdom 

Janet, P., Paris, France 

Nagaoka, H., Tokyo, Japan 

Kennelly. A. E., Cambridge. U.S.A. 

Ros, M. G., Zurich, Switzerland 

Dehalu, M., Liege, Belgiimi 

Rauszer, Z., Varsovy, Poland 

Fabry, C, Paris, France 

Siegbahn, M., Uppsala, Sweden 

de Broglie, L., Paris, France 

Cassinis, G., Milan, Italy 

Crittenden, E. C, Washington, D.C., U.S.A. 

de Haas, W. J., Leyden, The Netherlands 

Isnardi, T., Buenos Aires, Argentina 

Field, R. H., Ottawa, Canada 

Kouznetsov, A., Moscow, U.S.S.R. 

Danjon, A., Paris, France 

Vieweg, R., Braunschweig, Germany (Fed. Rep. of) 

Yamauti, Z., Tokyo, Japan 

de Boer, J., Amsterdam, The Netherlands* 

Nussberger, J., Prague, Czechoslovakia 

Astin, A. v.. Washington, D.C., U.S.A. 

Barrell, H., Teddington-London, United Kingdom 

Bourdoim, G. D., Moscow, U.S.S.R. 

Esserman, N. A.. Chippendale-Sydney, Australia 

Otero, J. M., Madrid, Spain* 



1897 

1897 

1900 

1900 

1901 

1901 

190;i 

1905- 

1907 

1907- 

1909 

1919. 

1919 

1919 

1919 

1921 

1921 

1922 

1923 

1923 

1927 

1928- 

1928- 

1928 

1928 

1929 

1929- 

1929- 

1930' 

1931. 

1931 

1933- 

1933- 

1936- 

1936 

1937- 

1939- 

1946- 

1946- 

1946- 

1946- 

1948- 

1951- 

1951- 

1952- 

1952- 

1952- 

1953- 

1953- 

1954- 

1954 

1954 

1954 

1954 



•1918 
■1904 
•1902 
■1921 
1919 
1931 
1908 
1931 
1914 
■1931 
■1917 
1930 
■1929 
■1926 
1940 
1950 
■1929 
1940 
■1927 
1965 
1929 
1941 
1952 
•1935 
•1935 
1948 
1958 
■1943 
1954 
■1937 
1948 
1939 
1954 
1952 
•1945 
1945 
1959 
1951 
1964 
1954 
1951 
1966 
1954 
1954 
1964 
1965 
1967 

1970 
1969 
1966 
1966 
1962 



•Present Member of Ihe CIPM (January 197S) 



234 



StuUa-Gotz, J., Vienna, Austria 1954- 

Vaisala, Y., Turku. Finland 1954-1971 

Howlett, L. E., Ottawa, Canada 1955-1969 

Krishnan, K, S., New Delhi, India 1958-1961 

Sandoval Vailarta, M., Mexico City, Mexico* 1960- 

Lehany, F. J., Chippendale-Sydney, Australia* 1963- 

Kichlu, P. K., New Delhi, India 1964-1966 

Mare'chal, A., Paris, France* 1964- 

Siegbahn, K., Uppsala, Sweden* 1964- 

Kersten, M., Braunschweij;, Germany (Fed. Rep. of) 1965-1970 

Dunworth. J. V., Teddington-London, United Kingdom* 1966- 

Niewodniczanski, H., Krakow, Poland 1966-1968 

Novikov, 1. 1., Moscow, U.S.S.R. 1966-1969 

Cinlra do Prado. 1... Sao Paulo. Brazil* 1967- 

Tomonaga, Y.. Tokyo. Japan 1967-1973 

Verma, A. R., New Delhi. India* 1967- 

Branscomb. L. M., Washington, D.C., U.S.A. 1969-1972 

Honti. P., Budapest. Hungary* 1969- 

Issaev, B. M.. Moscow. U.S.S.R.* 1969- 

Preston-Thomas. H., Ottawa. Canada* 1969- 

Djakov, E., Sofia, Bulgaria* 1970- 

Stille, U.. Braunschweig. Germany* (Fed. Rep. of) 1970- 

Perlstain, A., Wabem-Beme, Switzerland* 1971- 

Ambler, E., Washington, D.C., U.S.A.* 1972- 

Sakurai. Y., Tokyo. Japan* 1974- 



Chairmen of the CIPM 



Ibanez, C. 
Foerster, W. 
Gautier, R.^ 
Volterra. V. 
Zeeman. P.^ 
Sears. J. E.' 
Danjon. A. 
Vieweg. R. 
Howlett, L. E. 
Otero, J. M. 



1875-1891 
1891-1920 

1920- 1921 

1921- 1940 
1940-1943 
1946-1954 
1954-1960 
1960-1964 
1964-1968 
1968- 



Vice-Chairmen of the CIPM 



Crittenden, E. C. 1952-1954 

Vieweg, R. 1954-1960 

Howlett, L. E. 1960-1964 

Otero. J. M. 1964-1968 

Dunworth, J. V. 1968- 



t 

'i 

!( 

5 

' ad interim 

' ad interim from 1946 to 1948 



573-106 O - 75 - 17 



235 



Secretaries of the CIPM 



Hirsch, A. 
Blasema, P. 
Hepiles, Sl.-C/ 
Bodola. L. de 
Isaachsen, D. 
Cabrera. B. 
Dehalu. M. 
CassiIli^. C. 
<le Boer, J. 



1875-1901 
1901-1918 
1918-1922 
1923-1926 
1927-1933 
1933-1941 
1916-I9S2 
1952-1962 
1962- 



Directors of the BIPM 



Govi.G. [Italian] 1875-1877 

Pemet.J.[SHiss]^ 1877-1879 

Broch,0.-J. [Norwegian] 1879-1889 

BenouJ.-R. [French] 1889-1915 

Guillaume, Ch.-Ed. [Swiss] 1915-1936 

Perard, A. [French] 1936-1951 

Volet, G. [Swiss] 1951-1961 

Terrien, J. [French] 1962- 



* aii inlerim from 1918 lo 1920 

* ad interim 



236 



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241 



Appendix 5 



Worldwide Expansion of the Metric System 



In 1875, at the time of founding the BIPM, the Metric System had been 
adopted or introduced into some 30 countries. In 1975, almost all the coun- 
tries in the world had adopted it or had started a metric reform based on 
the SI, thus leaving a hope that the world will be 100 percent metric at the 
end of the 20th century. (See fig. 1 on next page.) 



243 




Tongo 

Borbodos, Jomoico, Nauru 

(G> 
(Fl 

(E) 
(Dl 

Irelond, Singopo'e 

(C) 

United Kingdom 

Ethiopio, Nepol 

Saudi Arabio 

Kuwoil 

Iroq 

Greece 

India 

Sudon 

Chino (Republic of) 
Jordon 

Albanio, Jgpori 

Viei-Nom (Dem. Rep. of) 

Koieo (Rep. of) 

Koreo (Dem. Rep. of), Israel 

Egypt 

Lebonon, Syr.o 

Iron 

Turkey 

Chioo (People's Republic) 
Libyo 

Afghonislon 

Indonesio, Morocco, Thoiland 

Hoiti. Mnd'io (opt.)l 

Polond 

U S.S.R. 

Panona 

Kbmef Republic 
Viet-Nom (Rep. of) 
(B) 

Denmork. Iceland, San Morino 
Ph j lippines 

Angolo, Guineo-Bissou, Mozambique 
Guinea 

Poroguoy. lU, S.S.R. (opr.)I 

Madagascor [United Kingdom (opl.)l 

Tunisio 

Cameroon 

[Japan (opt.)) 

Finland 
(A) 
Cobo 

Cosio Rico 
Seychelles 
Sweden 
Mauritius 

Liectilenstein, Norway 

Hungary 

Yugoslavio 

Germany, Austria, Czechoslovokia 

Bolivia, Switzerland 

lU.S A. (opt. II 

Ecuador 

Romania 

Argentina 

Broiil, Peru, Uruguoy 
Italy 

Mexico, Venezuela 
Colombio. Monoco 
Portugol 

Spoin, Dominican Republic 

Chile 

Algeria 

Belgium, Lu; 



mbourg, Netherlands 



1790 1800 1820 1840 1860 1880 1900 1920 1940 1960 1975 



Figure 1. Expansion of the Metric System throughout the world since its creation in 1795. The 
dates are those of the adoption or introduction of the Metric System in various countries 
and not those of its complete usage, this often not occurring until after a more or less long 
delay. A: Central African Republic. Congo (Rep. of the). Ivory Coast, Dahomey. Gabon, 
Upper Volta, MaH, Mauritania, Niger, Chad; B: Guatemala. Honduras. Malta, Nicaragua, 
El Salvador, Zaire; C: South Africa. Kenya, Uganda, Pal^rstan. Tanzania: D: Bahrain, Bot- 
svifana. New Zealand, Rhodesia. Swaziland: E: Australia. Canada. Gibraltar, Papua and 
New Guinea, Sri Lanlca, Trinidad and Tobago, Zambia; F: Bermuda, Guyana (Rep. of), 
Malaysia, Nigeria; G: Cyprus, Fiji, Ghana, Somalia, 
opt: Adoption for optional use. 



244 



Appendix 6 



Publications of the Metre Convention Organs 



The scientific and metrological work accomplished during the last 
century by the CGPM, the CIPM, its Consultative Committees, and the 
BIPM is recorded in the following publications which constitute important 
documentation on scientific metrology. 

1. Comptes rendus des seances de la Conference Generale des Poids et Me- 
sures (14 volumes from 1889 to 1971). 

Reports on the work of the CIPM, its Consultative Committees, and 
the BIPM; general administrative and financial decisions concerning the 
operation of the BIPM; discussion and adoption of metrological resolutions 
of international import. (The transactions of the first nine CGPM's are also 
published in collection 4.) 

2. Proces-verbaux des seances du Comite International des Poids et Me- 
sures (65 volumes from 1875 to 1973). 

Administration of the BIPM and orientation of its work; detailed re- 
port of the director on the activity of the BIPM; examination of reports of 
the Consultative Committees, results of various international comparisons, 
and proposals to ue submitted to the CGPM. 

3. Consultative Committees (The transactions of each meeting of a Con- 
sultative Committee are given in a publication.) 

Report of the Consultative Committee (and possibly of its Working 
Groups) presented to the CIPM; reports on international comparisons car- 
ried out at the BIPM or under the auspices of the CIPM; communications 
on the principal metrological work carried out in the world's specialized 
laboratories. (Before 1960, these transactions were published as appen- 
dices to the Proces-Verbaux du C.I. P.M. The 7 Consultative Committees 
have held 51 meetings: CCE (13), CCP (7), CCT (10), CCDM (5), CCDS (7), 
ecu (4), CCEMRI (5 from 1959 to 1964; since 1969, this Consultative Com- 
mittee has comprised four independent Sections which have held seven 
meetings: Section I (2), Section II (2), Section III (2), Section IV (1)). 

4. Travaux et Memoires du Bureau International des Poids et Mesures (22 
volumes from 1881 to 1966). 

Detailed descriptions of the principal work and metrological studies 



245 



carried out at the BIPM since its founding. (Publication stopped in 1966 
and replaced by the following one.) 

5. Recueil de Travaux du Bureau International des Poids et Mesures (4 
volumes from 1966 to 1974). 

Collection of articles published by the physicists and metrologists of 
the BIPM in scientific and technical journals or in the form of internal re- 
ports. 

6. Certain documents pubhshed in the preceding collections are also 
published separately: Recents progres du Systeme metrique, Echelle Inter- 
national Pratique de Temperature, Systeme International d' Unites. 

7. Annual Reports 

Reports from the CIPM office to the Governments on the administra- 
tive and financial situation of the BIPM. 

All the preceding publications are edited under the care of the BIPM. 

The journal Metrologia, founded in 1965 and edited under the 
auspices of the CIPM, publishes articles on the work of scientific metrolo- 
gy carried out in the world; periodically, information is given on the activi- 
ties of the Metre Convention organs under the heading "News from the 
BIPM." 



246 



Appendix 7 



Abbreviations Used in This Volume 



AAEC 

AECL 
AEET 

AIEA 
ASMW 



BCMN 

BIPM 

CCDM 
CCDS 
CCE 
CCEMRI 

CCP 
CCPR 

CCT 

ecu 

CENS 

CGPM 
CIPM 
CNAM 
DAMW 

ETL 
lEN 

IKO 



Australian Atomic Energy Commission, Lucas Heights, 
Austraha 

Atomic Energy of Canada Limited, Chalk River, Canada 
Atomic Energy EstabHshment (formerly Bhabha Atomic 

Research Center), Trombay, India 
International Atomic Energy Agency, Vienna, Austria 
Amt fur Standardisierung, Messwesen und Warenprii- 

fung (formerly DAMW), BerHn, German Democratic 

Republic 

Bureau Central de Mesures Nucleaires (Euratom), Geel, 
Belgium 

International Bureau of Weights and Measures, Sevres, 
France 

Consultative Committee for the Definition of the Metre 

Consultative Committee for the Definition of the Second 

Consultative Committee for Electricity 

Consultative Committee for the Standards of Measure- 
ment of Ionizing Radiations 

Consultative Committee for Photometry (now CCPR) 

Consultative Committee for Photometry and Radiometry 
(formerly CCP) 

Consultative Committee for Thermometry 

Consultative Committee for Units 

Centre d'Etudes Nucleaires de Saclay, Gif-sur-Yvette, 
France 

General Conference for Weights and Measures 
International Committee for Weights and Measures 
Conservatoire National des Arts et Metiers, Paris, France 
Deutsches Amt fiir Messwesen und Warenpriifung (now 

ASMW), Berlin, German Democratic Republic 
Electrotechnical Laboratory, Tokyo, Japan 
Istituto Elettrotecnico Nazionale Galileo Ferraris, Turin, 

Italy 

Institut voor Kernphysik Onderzoek, Amsterdam, 
Netherlands 



247 



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stitute for Research, Production, and Application of 




Radioisotopes), Prague, Czechoslovakia 



U. S. GOVERNMENT PRINTING OFFICE : 1975 O - 573-106 



248 



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